. CRYSTALLOGRAPHY 


AN  ELEMENTARY  MANUAL  FOR  THE 
LABORATORY 


BY 

M.  EDWARD  WADSWOKTH,  A.  M.,  PH.  D.,  F.  G.  S., 

Dean  of  the  School  of  Mines  and  Professor  of  Mining  Geology  in  the  University  of 

Pittsburgh  ;  Late  President  of  the  Michigan  College  of  Mines  and  Dean  of 

the  School  of  Mines  and  Metallurgy  in  the  Pennsylvania  State  College. 


WITH  6 


TABLES,, 29  PLATES.  .AN  QJB12  FIGURES 


PHILADELPHIA  : 

JOHN    JOSEPH    McVEY 

1909 


COPYRIGHT,  1909, 
JOHN  JOS.  McVEY 


So  tbc  jflfcemotB  of 
JOSIAH  DWIGHT  WHITNEY,  LL.  D. 

STATE  GEOLOGIST  OF  CALIFORNIA  AND 
STURGIS-HOOPER  PROFESSOR  OF  GEOLOGY  IN 

HARVARD  UNIVERSITY. 
LINGUIST,  CHEMIST,  MINERALOGIST,  GEOLOGIST,  AND 

MINING  GEOLOGIST. 

ONE  OF  GOD'S  NOBLEST  WORKS, 

AN  HONEST  MAN. 


331235 


INTRODUCTION 


CRYSTALLOGRAPHY  can  be  studied  from  two  different 
view-points :  one  as  a  mathematical  science  with  its 
applications  both  in  the  instrumental  determination  of 
crystal  angles  and  in  their  mapping  or  projection  ;  the 
other  chiefly  as  an  observational  study  with  the  appli- 
cation of  some  simple  rules  that  will  enable  the  pros- 
pector and  laboratory  student  to  determine  the  crys- 
talline form  with  sufficient  accuracy  for  practical 
purposes  in  the  field  or  laboratory.  It  is  the  intention 
here  simply  to  devote  our  time  to  the  latter  practical 
purpose,  which  is  all  that  the  average  engineering  or 
science  student,  who  is  not  making  a  specialty  of 
Crystallography  and  Mineralogy,  has  time  to  accom- 
plish. 

In  the  study  of  this  subject  I  worked  out  a  course  of 
brief  lectures  in  1873,  and  used  them  in  laboratory 
work  at  Harvard  University.  Subsequently,  in  1876 
and  in  later  years,  they  were  given  in  connection  with 
my  lectures  upon  Mineralogy  in  that  institution. 
These  lectures  form  the  nucleus  of  this  little  work. 
With  but  little  modification  they  were  given  after- 

(v) 


yi  INTRODUCTION. 

wards  at  Colby  University,  1885-1887;  and  at  the 
Michigan  College  of  Mines  (formerly  the  Michigan 
Mining  School),  from  1887  for  a  number  of  years, 
until  I  turned  the  work  over  to  my  assistant,  Dr.  H. 
B.  Patton,  placing  my  lecture  notes  in  his  hands. 
The  principal  and  essential  features  of  these  lecture 
notes  were  the  rules  for  the  determination  of  the  forms 
by  the  relation  of  the  planes  to  the  crystallographic 
axes.  They  were  originally  worked  out  by  me  in 
1873,  and  I  have  never  seen  them  in  print  anywhere, 
except  when  Dr.  Patton  in  1893  published  the  lecture 
notes  he  had  used  at  the  Michigan  College  of  Mines. 
A  second  enlarged  edition  of  his  book  was  published 
by  Dr.  Patton  in  1896,  and  a  third  in  1905.  Un- 
fortunately, Dr.  Patton  failed  to  acknowledge  the 
source  whence  those  rules  were  obtained. 

It  has  been  my  intention  for  over  thirty  years  to 
elaborate  and  publish  my  notes  for  the  use  of  my 
students,  but  as  my  time  has  been  fully  occupied  in 
other  work,  principally  in  development  work  and  in 
executive  duties,  as  well  as  in  original  investigation, 
very  little  time  has  been  available  in  which  to  prepare 
my  notes  for  publication.  Even  now,  on  account  of 
the  present  demands  upon  my  time,  but  little  elabora- 
tion can  be  made.  These  notes  are  published  now 
primarily  for  use  in  my  own  classes,  containing  over 
one  hundred  students  in  Mineralogy.  It  is  hoped, 


INTRODUCTION.  v 

however,  that  they  will  be  useful  to  other  teachers, 
who,  under  similar  circumstances,  are  required  to  give 
instruction  in  Crystallography,  Mineralogy,  and  kin- 
dred sciences,  as  a  means  to  an  end,  and  not  as  subjects 
to  be  studied  purely  for  themselves.  Such  a  practical 
purpose  cornes  naturally  as  the  result  of  the  present 
tendency  of  industrial  education.  It  is  now  required 
that  the  fundamental  sciences  be  reduced  to  the  mini- 
mum, in  order  that  in  four  years  the  student  may  re- 
ceive not  only  his  general  culture  and  intellectual  fur- 
nishing, but  that  he  may  also  obtain  the  maximum 
amount  of  training  in  the  practical  application  of  the 
sciences  to  his  future  engineering  or  technical  occupa- 
tion. 

My  notes  have  been  presented  in  the  form  of  lectures 
in  THE  PENNSYLVANIA  STATE  COLLEGE  since  1901,  and 
until  recently  I  have  followed  the  more  common  cus- 
tom of  starting  with  the  Isometric  System;  but  exper- 
ience has  led  me  to  believe  it  is  best  to  develop  the 
work  in  the  reverse  order,  beginning  with  the  Tri- 
clinic  System.  While  the  original  notes  form  the 
essential  basis  of  this  work,  there  will  be  this  differ- 
ence :  the  original  notes  for  lecture  purposes  formed 
simply  a  skeleton,  and  any  additional  explanations 
were  given  orally  by  the  instructor.  In  the  case  of 
this  book  the  necessary  explanatory  matter  has  been 
added  to  a  considerable  extent. 


INTRODUCTION. 

Instruction  in  Crystallography  presupposes  the  use 
of  a  collection  of  natural  crystals  and  of  crystal  models, 
as  well  as  personal  instruction  in  the  laboratory.  In 
case  such  collections  can  not  be  had,  models  can  be 
cut  out  of  soft  wood  like  cedar,  or  out  of  chalk.  They 
can  be  made  also  from  putty  or  clay  and  dried.  Per- 
ishable ones  can  be  cut  out  of  potatoes  or  turnips  or 
some  other  suitable  vegetable. 

The  glass,  paper  and  wooden  models  for  sale  by  Dr. 
F.  Krantz,  Bonn-am-Rhein,  Germany,  and  other  Ger- 
man dealers,  are  excellent,  and  every  laboratory 
should  be  well  stocked  with  them.  Smaller  collec- 
tions are  for  sale  by  the  Foote  Mineral  Company, 
Philadelphia ;  Otto  Kuntze,  Iowa  City,  Iowa ;  and 
Ward's  Natural  Science  Establishment,  Rochester, 
N.  Y.  The  larger  foreign  collections  can  be  imported 
by  the  above-mentioned  firms,  as  well  as  by  others,  for 
the  institutions  or  individuals  desiring  them.  Natural 
Crystals  can  be  obtained  from  the  above  firms  or  from 
any  other  dealers  in  minerals. 

The  methods  of  instruction  I  have  employed  in 
Crystallography  and  Mineralogy  were  detailed  in  a 
paper  read  before  the  Society  of  Naturalists  in  1883, 
and  published  in  the  Popular  Science  Monthly  during 
the  following  year  (pages  454-459).  After  a  long  ex- 
perience with  these  methods  it  appears  that  the  best 
results  have  been  obtained  by  first  going  over  care- 


INTRODUCTION.  IX 

fully  one  crystal  system  and  studying  a  selected  set  of 
models  in  that  system.  After  the  pupil  has  familiar- 
ized himself  with  the  general  characters  and  forms  in 
that  system,  he  has  been  given  a  large  collection  of 
unlabeled  models  of  that  system.  After  working  them 
out,  he  has  then  been  given  an  individual  recitation 
upon  these  forms,  his  errors  have  been  corrected,  and 
all  points  of  obscurity  have  been  explained  to  him. 
The  same  method  has  then  been  followed  with  an- 
other system,  and  so  on,  until  the  entire  six  systems, 
including  their  twin  forms,  are  understood,  so  far  as 
the  crystal  models  are  concerned. 

The  student  has  then  been  assigned  drawers  con- 
taining models  of  every  system  mixed  together,  so  that 
he  will  learn  to  distinguish  the  forms  of  one  system 
from  those  of  another.  After  this  he  has  been  as- 
signed natural  crystals  belonging  to  each  system  for 
his  personal  study,  following  the  same  method  as  with 
the  models ;  and  then  he  has  been  handed  a  mixed  set 
of  natural  crystals  of  every  system.  The  method  will 
naturally  have  to  be  varied  in  each  case  according  to 
the  number  of  crystals  or  models  each  instructor  has 
at  his  disposal. 

There  seems  to  be  no  way  of  teaching  the  student 
to  know  the  things  he  is  studying  except  the  labora- 
tory or  field  method,  as  mere  theory  is  of  but  little 
avail  in  the  practice  of  the  engineer  or  mining 


X  INTRODUCTION. 

geologist,  when  he  needs  to  know  what  is  the  mineral 
he  has  found. 

The  student  who  wishes  to  carry  the  study  of  Crys- 
tallography further  will  find  help  in  the  excellent 
chapter  upon  this  subject  in  Brush  and  Penfield's 
"  Manual  of  Determinative  Mineralogy  and  Blowpipe 
Analysis,"  John  Wiley  &  Sons,  New  York,  or  in  the 
following  valuable  works : 

Bauerman,  "  Systematic  Mineralogy,"  Longmans,  Green 
&  Co.,  London,  1881. 

Dana,  "Text  Book  of  Mineralogy,"  3rd  Ed.,  John  Wiley 
&  Sons,  New  York,  1898. 

Gurney,  "Crystallography,"  Society  for  Promoting  Chris- 
tian Knowledge,  London.  No  date. 

Hilton,  "Mathematical  Crystallography,"  Clarendon 
Press,  Oxford,  1903. 

Kraus,  "  Essentials  of  Crystallography,"  Ann  Arbor,  1906. 

Lewie,  "Treatise  on  Crystallography,"  University  Press, 
Cambridge,  England,  1899. 

Miers,  "Mineralogy,"  Macmillan  &  Co.,  London,  1902. 

Miller,  "A  Tract  on  Crystallography,"  Deighton,  Bell  & 
Co.,  Cambridge,  England,  1863. 

Milne,  ' '  Notes  on  Crystallography  and  Crystallo-physics, ' ' 
Trfibner  &  Co.,  London,  1879. 

Moses,  "The  Characters  of  Crystals,"  D.  Van  Nostrand 
Co.,  New  York,  1899. 

Moses  and  Parsons,  "Elements  of  Mineralogy,  Crystal- 
lography and  Blowpipe  Analysis,"  2nd  Ed.,  D.  Van 
Nostrand  Co.,  New  York,  1904. 


INTRODUCTION.  xi 

Patton,   "Lecture  Notes  on  Crystallography,"  3rd  Ed., 

D.  Van  Nostrand  Co..,  New  York,  1905. 
Story-Mask elyne,    "Crystallography,"    Clarendon   Press, 

Oxford,  1895. 
Williams,  "  Elements  of  Crystallography,"  Henry  Holt  & 

Co.,  New  York,  1890. 
Woodward,    "Crystallography  for  Beginners,"  Simpkin, 

Marshall,  Hamilton,  Kent  &  Co.,  London,  1896. 

In  the  German  and  the  French,  among  the  more 
recent  works, ,  the  attention  of  the  student  may  be 
called  to  the  following  : 

Bauer,  "Lehrbuch  der  Mineralogie,"  2  A.,  1904. 

Bravais,  "  Etudes  crystallographiques,"  1866. 

Brezina,  "  Methodik  der  Krystallbestimmung,"  1883. 

Bruhns,  "Elemente  der  Krystallographie,"  1902. 

Des  Cloizeaux,  "  Legons  de  cristallographie,"  1861. 

Frankenheim,  "  Zur  Krystallkunde,"  1869. 

Friedel,  "Cours  de  Mineralogie,"  1893. 

Goldschmidt,    ' *  Krystallographische    Projection  sbilder," 

1887. 
Goldschmidt, "  Index  'der  Krystallformen  der  Mineral- 

ien,"  1886-1891. 

Groth,  u  Physikalische  Krystallographie,"  1905. 
Hecht,  "Anleitung  zur  Krystallberechnung,"  1893. 
Heinrich,  "  Lehrbuch  der  Krystallberechnung, "  1886. 
Hochstetter  and  Bisching,  "Leitfaden  der  beschreibenden 

Krystallographie,"  1868. 


Xii  INTRODUCTION. 

Joerres,  "Eine  Abhandlung  tiber  Krystallographie,"  von 
W.  H.  Miller,  1864. 

Karsten,  "  Lehrbueh  der  Krystallographie,"  1861. 

Klein,  "Einleitung  in  die  Krystallberechnung,"  1876. 

Klockmann,  "  Lehrbuch  der  Mineralogie,"  4  A.,  1907. 

Knop,  "System  der  Anorganographie,"  1876. 

Kobell,  "Zur  Berechnung  der  Krystallformen,"  1867. 

Kopp,  "Einleitung  in  die  Krystallographie,  mit  einem 
Atlas,"  1862. 

Krefei,  "  Eleraente  der  mathematischen  Krystallog- 
raphie," 1887. 

Lang,  "  Lehrbuch  der  Krystallographie,"  1866. 

Lapparent,  "Cours  de  Mineralogie,"  3rd  Ed.,  1899. 

Liebisch,  u  Geometrische  Krystallographie,"  1881. 

Liebisch,  "  Physikalische  Krystallographie,"  1891. 

Liebisch,  "  Grundriss  der  physikalischen  Krystallog- 
raphie," 1896. 

Linck,  "Grundriss  der  Krystallographie,"  1896. 

Lion,  "  Trait6  616mentaire  cristallographie  g6ometrique," 
1891. 

Mallard,  "Trait6  der  cristallographie,"  1879. 

Martius-Matzdorff,  "Die  Elemente  der  Krystallogra- 
phie," 1871. 

Naumann-Zirkel,  "Elemente  der  Mineralogie,"  14  A., 
1901. 

Nies,  "  Allgemeine  Krystallbeschreibung,"  1895. 

Quenstedt,  "  Grundriss  der  bestimmenden  und  rechnenden 
Krystallographie,"  1873. 

Renard  et  Stoeber,  "  Notions  de  Mineralogie,  1900. 


INTRODUCTION.  Xlll 

Rose-Sadebeck,  "  Elemente  der  Krystallographie, ' '  Band 

L,  1873. 

Sadebeck,  "Angewandte  Krystallographie,"  1876. 
Schoenflies,     "  Krystallsysteme    und     Krystallstructur," 

1891. 

Scbrauf,  "  Lebrbuch  der  Krystallographie,"  1866. 
Sohncke,     "  Entwicklung    einer    Theorie   der    Krystall- 

structur,"  1879. 

Sommerfeldt,  u  Geometrische  Kristallograpbie,"  1006. 
Sommerfeldt,  "  Physikalische  Kristallograpbie,"  1907. 
Soret,  "  Elements  de  crystallographie  physique,"  1893. 
Tschermak,  "Lebrbuch  der  Wineralogie,"  6  A.,  1905. 
Twrdy,  "Methodischer  Lehrgang  der    Kristallographie," 

1900. 

Viola,  "Grundzuege  der  Kristallograpbie,"  1904. 
WebBky,  "Anwendung  der  Linearprojection  zur  Berech- 

nung  der  Krystalle,"  1886. 
Werner,  "  Leitfaden  zum  Studium  der  Krystallographie," 

1867. 
VViilfing,    "  Tabellarische   Uebereicht  der  einfachen   For- 

men   32    krystallographischen   Symmetriegruppen," 

1895. 
WyroubofT,  "  Manuel  pratique  de  cristallographie,"  1888. 

To  many  of  the  older  works,  especially  those  of 
Miller  and  Naumann,  every  student  of  Crystallography 
needs  to  refer,  as  well  as  to  the  writings  of  James  D. 
Dana.  The  author  has  been  indebted  greatly  not 
only  to  them,  but  also  to  very  many  of  the  works  cited 
above,  and  to  the  lectures  and  writings  of  Cooke. 


xiv  INTRODUCTION. 

Obviously  the  training  in  Crystallography,  as  in 
every  other  subject,  should  not  proceed  by  making 
the  principles  obscure,  but  rather  by  having  them 
clearly  and  easily  understood.  The  student  should 
obtain  his  knowledge  of  the  subject  and  his  mental 
discipline  by  applying  these  principles  in  actual  prac- 
tice. In  the  practical  application  he  should  be  thor- 
oughly questioned  to  see  that  he  has  not  only  mastered 
the  principles  but  can  readily  and  understandingly 
apply  them  in  the  laboratory  and  field. 

The  text  in  "  Language  Studies  "  and  the  examples 
in  Mathematics  furnish  laboratory  practice  for  students 
in  those  subjects,  but  in  "  Nature  Studies  "  the  objects 
must  be  supplied  and  worked  over  in  the  laboratory 
or  field ;  otherwise  the  pupil  better  be  employed  in 
learning  one  of  Webster's  orations,  instead  of  mem- 
orizing words  that  he  knows  nothing  about.  Recita- 
tion in  "  Science  Study  "  without  laboratory  or  field 
training  amounts  to  mere  declamation,  whether  the 
teaching  is  given  in  the  primary  school  or  in  the  col- 
lege or  university. 

To  repeat :  the  study  of  Crystallography  with  models 
and  natural  crystals  can  be  made  pleasant  and  inter- 
esting, but  without  them  the  study  is  in  the  nature  of 
a  farce — unless  pursued  purely  as  a  branch  of  Mathe- 
matics. Similar  methods  to  those  mentioned  for 
Crystallography  I  have  employed  with  excellent  re- 


INTRODUCTION.  XV 

suits  in  Mineralogy  and  Petrography ;  and  by  my 
direction  they  were  used  with  similar  satisfactory 
results  in  the  study  of  Zoology  and  Paleontology, 
taught  by  my  assistant,  now  Professor,  A.  E.  Seaman, 
at  the  Michigan  College  of  Mines.  These  principles 
seem  capable  of  a  much  more  extended  use  in  scien- 
tific, technical,  and  practical  education.  It  is  my 
expectation  to  publish  similar  lecture  notes  on  Min- 
eralogy and  Petrography. 

In  a  subject  so  thoroughly  worked  over  as  Crystal- 
lography has  been,  nothing  original  can  be  expected 
in  so  elementary  a  text  as  this,  except  possibly  in  its 
effort  to  lessen  the  student's  labor  and  thus  save  him 
time.  If  it  can  enable  engineering  and  scientific 
students  to  grasp  readily  as  much  of  the  principles  of 
Crystallography  as  they  need  for  their  subsequent 
Mineralogical  work,  its  purpose  will  have  been  accom- 
plished. The  first  nine  chapters  are  intended  to  be 
used  for  laboratory  work  and  for  recitation,  and  the 
last  three  for  reference  and  illustration. 

In  trying  to  make  matters  clear  to  a  student  one  is 
apt  to  forget  that  the  pupil  has  not  the  same  familiar- 
ity with  the  various  steps  in  the  process  as  has  the 
writer.  This  book  is  an  attempt  to  smooth  the  way 
for  the  pupil  as  far  as  practicable. 

The  author  will  be  very  glad  to  receive  the  sug- 
gestions of  other  teachers  of  this  subject,  and  will  be 


XVI  INTRODUCTION. 

sincerely  grateful  to  anyone  who  will  point  out  to  him 
such  parts  of  his  book  as  are  not  entirely  clear  or 
accurate. 

M.  EDWARD  WADSWORTH. 
THE  PENNSYLVANIA  STATE  COLLEGE, 
State  College,  Pa., August   12,  1909. 


TABLE  OF  CONTENTS 


PAGE 

INTRODUCTION v-xvi 

Origin  of  these  Notes v-vii 

Rules  for  Determining  Forms vi 

Need  of  Laboratory  Collections viii 

Methods  of  Instruction viii,  ix,  xiv,  xv 

Literature x-xiii 

Application  of  Principles xv,  xv 

CHAPTER    I 

PRELIMINARIES     1-8 

Natural  World - 1 

Mineral  Kingdom  or  Mineralogy 1 

Vegetable  Kingdom  or  Botany  ^ 

>  Biology 1 

Animal  Kingdom  or  Zoology     J 

Mineralogy 1,  2 

Mineral  Chemistry .  2 

Optical  Mineralogy 2 

Crystallography 2 

Minerals  and  Crystals 3-6 

Distortion  of  Forms  .  , .  3 

Uniformity  of  Inclination  of  Faces 3 

Locating  Points 3-6 

Axes 6 

Nomenclature 6 

Octants 7 

(l) 


TABLE    OF    CONTENTS. 

PAGE 

Crystal lographic  Systems      7,  8 

Triclinic 7 

Monoclinic 7 

Orthorhombic 7 

Tetragonal 7 

Isometric 7 

Hexagonal 8 

CHAPTER  II 

THE  TRICLINIC  SYSTEM 9-39 

Its  Axes  and  Angles 9 

Nomenclature 10 

Relation  of  Planes  to  the  Axes 10 

Vertical  Axis 10 

Lateral  Axes 10 

Brachy-Axis ,    .        10 

Macro-Axis 10 

Pinacoids 11 

Vertical  Pinacoids  or  Basal  Pinacoids 11 

Brachy-Pinacoids 11,  12 

Macro-Pinacoids 12 

Domes  and  Prisms 12 

Brachy-Domes ,    .    .    .        12 

Macro-Domes 12 

Vertical  Domes  or  Prisms 12 

Pyramids  or  Octahedrons 12,  13 

Axial  Models  .    .       13 

Similar  Axes,  Planes,  Edges,  and  Angles 13, 14 

Symmetry 14-19 

Illustration  of  the  Term 14-17 

Plane  of  Symmetry 15-18 

Axes  of  Symmetry 18,19 

Binary  Symmetry 18 

(2) 


TABLE   OF   CONTENTS. 

PAGE 

Trigonal  Symmetry 18, 19 

Tetragonal  Symmetry 18 

Hexagonal  Symmetry 18 

Centre  of  Symmetry 19 

Distinguishing  Characteristics  of  the  Triclinic  Crystals 19-21 

Distinction  from  other  Systems 19-21 

Obliquity  of  Planes  and  Edges 20,21 

Wedge-shaped  Forms 20,  21 

Position  of  Axes 21 

Rules  for  naming  Triclinic  Planes 21,  22 

Pinacoids 21 

Domes  and  Prisms 21,  22 

Pyramids  or  Octahedrons , 22 

Forms 22-28 

Holohedral  Forms 23 

Hemihedral  Forms    . 24,  25 

Tetartohedral  Forms 25 

Simple  and  Compound  Crystals 25-28 

Dominant  Forms 26 

Subordinate  Forms 26 

Modification 26-28 

Replacement 26-28 

Truncation 27 

Bevelment 27,  28 

Beading  Crystallographic  Drawings 28-34 

Notation  of  Weiss 28-32 

u         "  Naumann 32,  33 

"        u  J.  D.  Dana 32,  33 

u  Miller 32-34 

"Levy 29 

Axial  Notation 29-34 

Parameters •  .    .  31-33 

Indices 32-34 

(3) 


TABLE    OF    CONTENTS. 

PAGE 

Positive  and  Negative  Symbols 33,  34 

Comparative  Table  of  Triclinic  Notations 35 

Table  I 

Hemihedral  and  Tetartohedral  Notations 36-38 

Directions  for  Studying  Triclinic  Crystals 38,  39 

CHAPTER  III 

MONOCLINIC  SYSTEM 40-49 

Its  Axes  and  Angles 40 

Symmetry 40,41 

Plane  of  Symmetry 40 

Axis  of  Binary  Symmetry .......        41 

Centre  of  Symmetry 41 

Nomenclature 41-43 

Axes 41,42 

Vertical  Axis 4   •    •"  •        41 

Lateral  Axes 41,  42 

Ortho-Axis      42 

Clino-Axis  ....  .....  -.„.;.  .   /.        42 

Pinacoids 42,  43 

Vertical  Pinacoids  or  Basal  Pinacoids 42 

Clino-Pinacoids 43 

Ortho-Pinacoids 43 

Domes  and  Prisms      43 

Clino-Domes       43 

Ortho-Domes 43 

Vertical  Domes  or  Prisms 43 

Pyramids  or  Octahedrons 43 

Relation  of  Planes  to  Axes ...;*-..    ...        43 

Distinguishing  Characteristics  of  the  Monoclinic  Crystals     ...        44 

Rules  for  naming  Monoclinic  Planes 44,  45 

Pinacoids 44 

(4) 


TABLE    OF    CONTENTS. 

PAGE 

Domes  and  Prisms 44 

Pyramids  01  Octahedrons 45 

Forms 45,  46 

Holohedral  Forms 45 

Hemihedral  Forms 45 

Hemimorphic  Forms 45,  46 

Clinohedral  or  Pseudo-hemimorphic  Forms 46 

Compound  Forms 46 

Reading  Drawings  of  Monoclinic  Crystals 46-48 

Comparative  Table  of  Monoclinic  Notations 48 

Table  II 48 

Directions  for  studying  Monoclinic  Crystals 49 

CHAPTER  IV 

ORTHOBHOMBIC  SYSTEM 50-59 

Its  Axes  and  Angles  ....       , 50 

Nomenclature 50, 5l 

Axes .  .  7  .  ,  V  .   .    .        50 

Vertical  Axis  . 50 

Lateral  Axes 50 

Brachy-Axis 50 

Macro-Axis 50 

Pinacoids 50 

Vertical  Pinacoids  or  Basal  Pinacoids 50 

Brachy-Pinacoids 50 

Macro-Pinacoids 50 

Domes  and  Prisms 50,51 

Brachy-Domes 50,  51 

Macro-Domes 50,  51 

Vertical  Domes  or  Prisms 50, 51 

Pyramids  or  Octahedrons 51 

Relation  of  Planes  to  Axes 51 

Symmetry 51,  52 

(5) 


TABLE    OF    CONTENTS. 

PAGE 

Distinguishing  Characteristics  of  the  Orthorhombic  Crystals.  53,  54 

Kules  for  Naming  Orthorhombic  Planes 54 

Pinacoids 54 

Domes  and  Prisms 54 

Pyramids  or  Octahedrons :    .        54 

Forms 54-57 

Holohedral  Forms 54,  55 

Symmetry 55 

Hemihedral  Forms 55, 56 

Sphenoids ....  55,  56 

Symmetry 55 

Hemimorphic  Forms 56 

Symmetry 56 

Compound  Forms 57 

Holohedral  Forms  .      57 

Hemihedral  Forms 57 

Hemimorphic  Forms 57 

Beading  Drawings  of  Orthorhombic  Crystals 57,58 

Comparative  Table  of  Orthorhombic  Notations 58 

Table  III 58 

Directions  for  Studying  Orthorhombic  Crystals 59 

CHAPTEK   V 

TETRAGONAL  SYSTEM 60-72 

Its  Axes  and  Angles 60 

Nomenclature 60-62 

Axes 60 

Vertical  Axis 60 

Lateral  Axes 60 

Pinacoids        60 

Vertical  or  Basal  Pinacoids i'  .   .   .        60 

Prisms ,   .   .        61 

Primary  Prisms  or  Prisms  of  the  First  Order 61 

(6) 


TABLE   OF   CONTENTS. 

PAGE 

Secondary  Prisms  or  Prisms  of  the  Second  Order    ...        61 

Ditetragonal  or  Dioctahedral  Prisms 61 

Pyramids  or  Octahedrons .    •  61 ,  62 

Primary  Pyramids  or  Pyramids  of  the  First  Order  .  .  61 
Secondary  Pyramids  or  Pyramids  of  the  Second  Order.  61,  62 
Ditetragonal  Pyramids  or  Dioctahedrons  or  Zirconoids.  62 

Kelation  of  Planes  to  Axes 62 

Distinguishing  Characteristics  of  Tetragonal  Crystals 62 

Kules  for  Naming  Tetragonal  Planes 62,  63 

Pinacoids 62,  63 

Domes  and  Prisms 63 

Pyramids  or  Octahedrons 63 

Forms 63-69 

Holohedral  Forms 63-65 

Symmetry 64 

Relations  and  Numbers  of  Prisms  and  Pyramids     ...        65 

Hemihedral  Forms .    ._  ........  65-69 

Sphenoidal  Group 65-67 

Sphenoids 65-67 

Tetragonal  Scalenohedrons  .    .    .   . 66,67 

Symmetry .......        67 

Pyramidal  Group 67-69 

Tertiary  Prisms  or  Prisms  of  the  Third  Order     .    .        67 
Tertiary  Pyramids  or  Pyramids  of  the  Third  Order  67, 68 

Symmetry 68 

Tetragonal  Trapezohedrons 69 

Right-Handed  or  Positive    .    .   .    .    .......        69 

Left-Handed  or  Negative 69 

Symmetry 69 

Compound  Forms 69 

Reading  Drawings  of  Tetragonal  Crystals 69,  70 

Comparative  Table  of  Tetragonal  Notation 71 

(7) 


TABLE   OF    CONTENTS. 

PAGE 

TablelV 71 

Directions  for  Studying  Tetragonal  Crystals 72 

CHAPTER  VI 

HEXAGONAL  SYSTEM 73-121 

Its  Axes  and  Angles 73 

Relations  of  the  Hexagonal  and  Tetragonal  Systems  .      .    .  73, 74 

Symmetries  of  both  Systems 74 

Divisions  of  the  Hexagonal  System 74 

Hexagonal  Division 74 

Rhombohedral  (Trigonal)  Division 74 

Miller-Bravais  Indices 75 

Modernized  Weiss  Parameters 75 

Nomenclature 75 

Relations  of  Planes  to  Axes 75 

Distinguishing  Characteristics  of  Hexagonal  Crystals     ...        76 
Principal  Forms  of  the  Hexagonal  System   ...       ....  76-80 

Holohedral  Forms 80-85 

Basal  Pinacoid 80 

Primary  Hexagonal  Prism 80, 81 

Secondary  Hexagonal  Prism 81 

Dihexagonal  Prism 81 

Primary  Hexagonal  Pyramid 81 

Secondary  Hexagonal  Pyramid 82 

Dihexagonal  Pyramid 82 

Relations  of  the  Primary  and  Secondary  Hexagonal  Prisms 

and  Pyramids 82-85 

Parameters  of  the  Secondary  Prisms  and  Pyramids    ....  82-84 
Symmetry  of  the  Holohedral  Forms 84,  85 

Hemihedral  Forms 85-96 

Rhombohedral  Group 85-91 

Primary  Rhombohedron 85-88 

(8) 


TABLE    OF    CONTENTS. 

PAGE 

Positive  Rhombohedron 85 

Negative  Khombohedron ;"...• 85, 86 

Terminal  Edges      86 

Lateral  Edges    ..-.;       >,> 86 

Solid  Angles   .   .   .   ,   .   ^ 86 

Acute  Rhombohedron 87 

Obtuse  Rhombohedron 87 

Principal  Rhombohedron 87 

Subordinate  Rhombohedron 87 

Rhombohedral  Truncation .  87, 88 

Hexagonal  Scalenohedron 88-90 

Positive  Scalenohedron 88-90 

Negative  Scalenohedron 88-90 

Distinction  between  the    Hexagonal    and    Tetragonal 

Scalenohedrons 89 

Lateral  Edges 89 

"  Saw  Teeth" 89 

Distinction  between  Positive  and  Negative  Scalenohe- 
drons     89,90 

Inscribed   Rhombohedrons  or   Rhombohedrons  of  the 

Middle  Edges 90 

Relation  of  the  Rhombohedron  and  the  Scalenohedron.        90 

Number  of  Scalenohedrons 90 

Symmetry  of  the  Rhombohedral  Group 90,  91 

Pyramidal  Group 91-93 

Tertiary  Hexagonal  Prism 91,92 

Relation  of  the  Tertiary  to  the  Primary  and  Secondary 

Hexagonal  Prisms 91 

Positive  or  Right-handed  Prism  .  .    . 92 

Negative  or  Left-handed  Prism  . 92 

Symbols  for  these  Forms 92 

Tertiary  Hexagonal  Pyramid .   .  -  .    .    .  92,  93 

(9) 


TABLE    OF    CONTENTS. 

PAGE 

Positive  or  Right-handed  Pyramid 92 

Negative  or  Left-handed  Pyramid 92 

Relation    of   the  Tertiary   to    the    Primary    and    Secondary 

QQ 

Hexagonal  Pyramids 

Symmetry  of  the  Pyramidal  Group 9£ 

Hexagonal  Trapezohedral  Group 93-95 

Positive  or  Eight-handed  Hexagonal  Trapezohedron     ...        94 
Negative  or  Left-handed  Hexagonal  Trapezohedron  ....        94 

Symmetry  of  the  Trapezohedral  Group 04 

Distinction  from  the  Scalenohedron 94 

Distinction  of  the  Right-handed  from  the  Left-handed  .   .    .  94,  95 

Trigonal  Group 95,  96 

Ditrigonal  Pyramid 95 

Positive 95 

Negative 95 

Symmetry 96 

Tetartohedral  Forms 96-102 

Rhombohedral  Group 96-98 

Secondary  Rhombohedron 96,  97 

Relation  to  the  Primary  Rhombohedrons 97 

Positive  and  Negative 97 

Right-handed  and  Left-handed 97 

Tertiary  Rhombohedron 97 

Relation  to  the  Primary  and  Secondary  Rhombohe- 
drons     97,  98 

Symmetry  of  the  Secondary  and  Tertiary  Rhombohe- 
drons             98 

Trapezohedral  Group 98-100 

Secondary  Trigonal  Prism 99 

Positive  or  Right-handed 99 

Negative  or  Left-handed 99 

Ditrigonal  Prism 99 

(10) 


TABLE    OF    CONTENTS. 

PAGE 

Positive  or  Eight-handed 99 

Negative  or  Left-handed  .    .    .   . 99 

Secondary  Trigonal  Pyramid 99, 100 

Positive  or  Right-handed 99 

Negative  or  Left-handed 99 

Trigonal  Trapezohedron 100 

Negative  Eight-  or  Left-handed 100 

Positive  Eight- or  Left-handed 100 

Symmetry  of  the  Trapezohedral  Group 100 

Trigonal  Group .   -  .  -- 101,102 

Primary  Trigonal  Prism ' 101 

Positive 101 

Negative 101 

Tertiary  Trigonal  Prism 101,102 

Positive  Eight- or  Left-handed 101,102 

Negative  Eight-  or  Left-handed 102 

Primary  Trigonal  Pyramid 102 

Positive    .    .    .   . 102 

Negative...   .   .   < 102 

Tertiary  Trigonal  Pyramid 102 

Positive  Eight-  or  Left-handed   . 102 

Negative  Eight-  or  Left-handed 102 

Symmetry    ....   .   v,   ......  v 102 

Hemimorphic  Forms 102-104 

lodyriteType .102,103 

Symmetry 103 

Nephelite  Type 103 

Symmetry 103 

Tourmaline  Type  .    .."..,.,.   .  :   . 103 

Symmetry    .    ...    /  ..    . 103 

Sodium  Periodate  Type    .    .    .    ...... 103, 104 

Symmetry 104 

(ID 


TABLE    OF   CONTENTS. 

PAGE 

Compound  Forms 104 

Rules  for  Naming  Hexagonal  Planes 104-109 

Pinacoids 104 

Prisms 104-106 

Pyramids 106-108 

Rhombohedrons 106-108 

Scalenohedrons 107 

Trapezohedrons 107, 108 

Hemimorphic  Forms 108,  109 

Reading  Drawings  of  Hexagonal  Crystals 109-113 

Lettering  Semi-axes 109 

Parameters  or  Indices 110,  111 

Miller-Bravais  Notation 110-112 

Weiss  Notation Ill 

Naumann  Notation 111-113 

Dana  Notation 112 

Notation  of  Ehombohedron  and  Scalenohedron 112 

Notation  of  Hemimorphic  Forms 112,113 

Hexagonal  Forms  and  Notations 114-120 

Table  V 114-120 

Directions  for  Studying  Hexagonal  Crystals 121 

CHAPTER  VIJ 

ISOMETRIC  SYSTEM 122-147 

Axes 122 

Nomenclature 122, 123 

Semi-Axes 122 

Distinguishing  Characteristics  of  the  Isometric  Crystals  .  .  123 
Forms  of  the  Isometric  System 123-125 

Holohedral  Forms •  .  .  .  .  125-131 

Hexahedron  alias  Cube  .  .  .  , 126 

Dodecahedron ....  126  127 

(12) 


TABLE   OF    CONTENTS. 

PAGE 

Tetrakis  Hexahedron    .   .       127 

Octahedron 127, 128 

Trigonal  Triakis  Octahedron .    .  ' 128, 129 

Tetragonal  Triakis  Octahedron L  .   .   .      129 

Hexakis  Octahedron 130 

Symmetry 130, 131 

Cubic  Axes  . 131 

Octahedral  Axes 131 

Dodecahedral  Axes .    .   ..?..,.      131 

Hemihedral  Forms .131-139 

Oblique  Hemihedral  Forms -..'>,*.  •    •   •      131-135 

Tetrahedron 132 

Positive 132 

Negative. .-.   , 132 

Tetragonal  Triakis  Tetrahedron     .   .   .   *  .   .    .   .    .  132, 133 

Positive 133 

Negative 133 

Trigonal  Triakis  Tetrahedron 133, 134 

Hexakis  Tetrahedron -.  •*   .   .   .    .   .134,135 

Positive 135 

Negative 135 

Symmetry 135 

Parallel  Hemihedral  Forms 135-138 

Pentagonal  Dodecahedron 135-137 

Positive 136, 137 

Negative.   .   .  ......   ..  .  »->:...  %   .   .    .136,137 

Dyakis  Dodecahedron 137,138 

Positive 137 

Negative 137 

Symmetry    .    - 138 

Gyroidal  Hemihedral  Forms 138, 139 

Pentagonal  Icositetrahedron 138,  139 

(13) 


TABLE    OF    CONTENTS. 

PAGE 

Eight-handed 138, 139 

Left-handed 138,  139 

Symmetry 139 

Tetartohedral  Forms 140, 141 

Tetrahedral  Pentagonal  Dodecahedron     = 140, 141 

Positive  Eight-  or  Left-handed 140, 141 

Negative  Eight-  or  Left-handed 140, 141 

Symmetry 141 

Compound  Forms 141,142 

Holohedral  Compound  Forms 141 

Oblique  Hemihedral  Compound  Forms 141 

Parallel  Hemihedral  Compound  Forms 141 

Gyroidal  Hemihedral  Compound  Forms 142 

Tetartohedral  Compound  Forms .       142 

Eules  for  Naming  Isometric  Planes 142-144 

Cube 142 

Dodecahedron 143 

Tetrakis  Hexahedron        143 

Pentagonal  Dodecahedron 143 

Octahedron 143 

Tetrahedron 143 

Trigonal  Triakis  Octahedron 143 

Tetragonal  Triakis  Tetrahedron 143 

Tetragonal  Triakis  Octahedron 144 

Trigonal  Triakis  Tetrahedron 144 

Hexakis  Octahedron 144 

Hexakis  Tetrahedron 204 

Pentagonal  Icositetrahedron 144 

Dyakis  Dodecahedron  ...       144 

Tetragonal  Pentagonal  Dodecahedron 144 

Eeading  Drawings  of  Isometric  Crystals 145 

Isometric  Forms  and  Notations 146,  147 

(14) 


TABLE   OF    CONTENTS. 

PAGE 

Table  VI     . 146, 147 

Directions  for  Studying  Isometric  Crystals 147 

CHAPTER  VIII 
MINERAL  AGGREGATES,  PARALLEL  GROWTHS,  AND  TWINS    .  148-154 

Crystalline 148 

Amorphous 148 

Pseudomorphs 148 

Compound  Minerals  or  Crystals  ....        149, 150 

Mineral  Aggregate 149 

Parallel  Growths  or  Groups 149 

Twins 149, 153 

Reentrant  Angles 150, 151 

Striations 150, 151 

Oscillatory  Combination 151 

Polysynthetic  Twinning 151,  153 

Contact  Twinning 152, 153 

Composition  Plane 152 

Twinning  Axis 152 

Cyclic  Twins 153 

Penetration  Twinning 4   .....      153 

Mimicry „    .  153,  154 

CHAPTER  IX 

CLEAVAGE 155-160 

Nomenclature 155,  156 

Notation 156 

Triclinic  Cleavages 156 

Monoclinic  Cleavages 157 

Orthorhombic  Cleavages 157 

Tetragonal  Cleavages 157, 158 

Hexagonal  Cleavages 158 

Isometric  Cleavages 159 

(15) 


TABLE    OF    CONTENTS. 

PAGE 

Partings 159, 160 

Nomenclature 159 

Parting  Structure 159 

Cleavage  Structure • 159 

Mineral  Parting 160 

Parallel  Kock  Jointing 160 

Mineral  Cleavage 160 

Eock  or  Slaty  Cleavage 160 

CHAPTER  X 

CRYSTALLOGRAPHIC  SYMMETRY 161-166 

Symmetry  Drawings 161,162 

Notation 161,  162 

Triclinic  Symmetry 162 

Monoclinic  Symmetry 162 

Holohedral  Symmetry 162 

Clinohedral  or  Hemihedral  Symmetry 162 

Orthorhombic  Symmetry 162,  163 

Holohedral  Symmetry 162 

Hemihedral  Symmetry 162, 163 

Hemimorphic  Symmetry 163 

Tetragonal  Symmetry 163 

Holohedral  Symmetry 163 

Sphenoidal  Symmetry 163 

Pyramidal  Symmetry 163 

Trapezohedral  Symmetry J63 

Hexagonal  Symmetry 163-165 

Holohedral  Symmetry 163 

Hemihedral  Symmetry 164 

Rhombohedral  Symmetry 164 

Pyramidal  Symmetry 164 

Trapezohedral  Symmetry 164 

(16) 


TABLE    OF    CONTENTS. 

PAGE 

Trigonal  Symmetry 164 

Tetartohedral  Symmetry 164, 165 

Rhombohedral  Symmetry 164 

Trapezohedral  Symmetry 165 

Trigonal  Symmetry 164,  165 

Hemimorphic  Symmetry 165 

lodyrite  Symmetry 165 

Nephelite  Symmetry 165 

Tourmaline  Symmetry 165 

Sodium  Periodate  Symmetry 165 

Isometric  Symmetry 165, 166 

Holohedral  Symmetry 165 

Hemihedral  Symmetry 165, 166 

Oblique  Hemihedral  Symmetry 165 

Parallel  Hemihedral  Symmetry 166 

Gyroidal  Hemihedral  Symmetry 166 

Tetartohedral  Symmetry 166 

CHAPTER  XI 

THE  THIRTY-TWO  CLASSES  OF  CRYSTALS 167-186 

Triclinic  System V  ,.   .  . 167-169 

1.  Asymmetric  or  Hemihedral  Class 167,  168 

2.  Pinacoidal  or  Holohedral  Class     .  r 168,  169 

Monoclinic  System 169, 170 

3.  Sphenoidal  or  Hemimorphic  Class 169 

4.  Domatic  or  Hemihedral  Class    .  'I .  . ..._ 169,170 

5.  Prismatic  or  Holohedral  Class _       170 

Orthorhombic  System ..;.........  170-172 

6.  Bisphenoidal  or  Hemihedral  Class 170,  171 

7.  Pyramidal  or  Hemimorphic  Class    .    .  '.    .    .....    171 

8.  Bipyramidal  or  Holohedral  Class 171,172 

Tetragonal  System 172-176 

9.  Bisphenoidal  Tetartohedral  Class 172 

(17) 


TABLE    OF    CONTENTS. 

PAGE 

10.  Pyramidal  Class 172,173 

11.  Scalenohedral  or  Sphenoidal  Class 173,174 

12.  Trapezohedral  Class 174 

13.  Bipyramidal  Class 174, 175 

14.  Ditetragonal  Pyramidal  Class 175 

15.  Ditetragonal  Bipyramidal  Class 175,  176 

Hexagonal  System 176-183 

TRIGONAL  DIVISION   . 176-180 

16.  Trigonal  Pyramidal  or  Ogdohedral  Class 176, 177 

17.  Khombohedral  Class 177 

18.  Trigonal  Trapezohedral  Class 177,  178 

19.  Trigonal  Bipyramidal  Class 178 

20.  Ditrigonal  Pyramidal  Class 178, 179 

21.  Ditrigonal  Scalenohedral  Class 179 

22.  Ditrigonal  Bipyramidal  Class     .        179, 180 

HEXAGONAL  DIVISION 180-183 

23.  Hexagonal  Pyramidal  Class 180,  181 

24.  Hexagonal  Trapezohedral  Class 181 

25.  Hexagonal  Bipyramidal  Class 181,182 

26.  Dihexagonal  Pyramidal  Class 182 

27.  Dihexagonal  Bipyramidal  Class 182,  183 

Isometric  System 183-186 

28.  Tetrahedral  Pentagonal  Dodecahedral  Class    -    .    .  183. 184 

29.  Pentagonal  Icositetrahedral  Class      184 

30.  Dyakis  Dodecahedral  or  Parallel  Hemihedral  Class.  184,185 

31.  Hexakis  Tetrahedral  or  Oblique  Hemihedral  Class.  185,186 

32.  Hexakis  Octahedral  or  Holohedral  Class         ....      186 

CHAPTER  XII 

CRYSTALLOGRAPHIC  NOMENCLATURE 187-202 

Similarity  of  Personal  and  Crystallographic  Nomenclature.  187-189 

The  Families  of  the  Prism  Tribe     ....''.    /  189-193 

(18) 


TABLE   OF   CONTENTS. 

PAGE 

The  Family  of  Triclinic  Prisms 189,  190 

The  Family  of  Monoclinic  Prisms 190 

The  Family  of  Orthorhombic  Prisms 190,  191 

The  Family  of  Tetragonal  Prisms 191 

The  Family  of  Hexagonal  Prisms 191-193 

The  Families  of  the  Pyramid  Tribe 193-199 

The  Family  of  Triclinic  Pyramids  . 193 

The  Family  of  Monoclinic  Pyramids 193 

The  Family  of  Orthorhombic  Pyramids 194 

The  Family  of  Tetragonal  Pyramids 194-196 

The  Family  of  Hexagonal  Pyramids 196-199 

The  Families  of  the  Pinacoid  Tribe 199.200 

The  Families  of  the  Isometric  Tribe 200-202 

Description  of  the  Plates .203-261 

Plate  I,  Figs.  1-11 ...          203 

Plate          II,  Figs.  12-34 .   .  1''.   .   .   .  204,205 

Plate        III,  Figs.  35-55    ....   .    .  .   .   .    '.   .    .   .   .206,207 

Plate        IV,  Figs.  56-85    ...>-.." '.   .    .207-210 

Plate          V,  Figs.  86-112 .211-213 

Plate        VI,  Figs.  113-144 /  -.  •   i '•   •   •    •      213-215 

Plate       VII,  Figs.  145-169 216-218 

Plate     VIII,  Figs.  170-198 ....        .  218-220 

Plate        IX,  Figs.  199-220        ......    .221-223 

Plate          X,  Figs.  221-245 223-226 

Plate        XI,  Figs.  246-269  226-229 

Plate      XII,  Figs.  270-297 .       .   .   .    .229-232 

Plate     XIII,  Figs.  298-319    .   .   .   *,  .    .    .   ...  ,.V_.   .      232-234 

Plate     XIV,  Figs.  320-339    ......       ....'..      235,236 

Plate       XV,  Figs.  340-365 236-238 

Plate     XVI,  Figs.  366-385 238-240 

Plate    XVII,  Figs.  386-415 240-243 

Plate  XVIII,  Figs.  416-445 244-246 

(19) 


TABLE    OF    CONTENTS. 

PAGE 

Plate     XIX,  Figs.  446-472 247,248 

Plate       XX,  Figs.  473-500 248-250 

Plate     XXI,  Figs.  501-524 250-253 

Plate    XXII,  Figs.  525-548 253-255 

Plate  XXIII,  Figs.  549-580 255-258 

Plate  XXIV,  Figs.  581-595 258-260 

Plate    XXV,  Figs.  596-612 260,261 

Triclinic  Forms 203,  205,  206,  247,  249,  258,  261 

Monoclinic  Forms 203,  208-211,  248-250,  255,  258,  261 

Orthorhombic  Forms    .  203,  204,  211-216,  247,  250,  252,  256-259 
Tetragonal  Forms, 

203,  205,  206,  216-221,  224,  225,  251,  253,  259,  261 
Hexagonal  Forms  .  .  .  203-207,  215,  221-235,  249-255,  259,  260 
Isometric  Forms.  .  .  .203,204,207,208,251,236-248,253-261 

Errata 262,263 

Index , 265-299 

(20) 


NOTES  ON  CRYSTALLOGRAPHY 


CHAPTER  I 

PRELIMINARIES 

ALL  students  of  the  sciences  know  that  the  natural 
objects  of  this  earth  are  divided  into 'three  kingdoms  : 
Animal,  Vegetable,  and  Mineral  The  first  comprises 
all  animals  ;  the  second  includes  every  plant ;  and  the 
third  all  other  materials  such  as  minerals  and  min- 
eral aggregates,  or  rocks,  water,  air,  etc.  The  Animal 
and  Vegetable  Kingdoms  can  be  united  under  one  head 
called  the  Organic  World,  and  the  Mineral  Kingdom 
can  be  called  the  Inorganic  World. 

Our  knowledge  of  these  kingdoms  has  also  its  three- 
fold classification  :  Zoology  comprises  our  knowledge 
of  the  various  forms  of  animal  life ;  Botany  relates  to 
plant  life;  and  Mineralogy,  in  its  broadest  sense,  can 
be  held  to  cover  our  knowledge  of  the  inorganic  world. 

Botany  and  Zoology  together  are  united  under  the 
broader  term  Biology,  or  the  "  Science  of  Life  ". 

The  inquiring  student  will  find,  however,  that  in 


2  *;  ^'OTES'.pW  p&YSf  ALLOGRAPHY. 

its  mcV$:<^^ii  -'tfceegtanceHhe  term  Mineralogy  is 
not  used  in  its  broadest  or  most  universal  sense,  but  is 
rather  employed  to  comprise  our  knowledge  of  the 
simple  minerals,  when  that  term  is  used  with  a  re- 
stricted meaning.  If  this  limitation  is  applied,  a 
Mineral  may  be  defined  as  an  inorganic  body  which 
has  a  more  or  less  definite  chemical  composition  and 
internal  structure,  and  which,  as  a  rule,  tends  to  have 
a  definite  shape  or  form.  Mineral  Chemistry  is  the 
name  of  the  science  that  relates  to  the  chemical  com- 
position of  the  minerals ;  Optical  Mineralogy  is  the 
name  of  the  science  which  relates  to  the  internal 
structure  of  minerals  as  shown  by  their  effects  upon 
light.  The  form  that  a  mineral  tends  to  assume  is 
known  as  a  Crystal,  see  Fig.  10,  and  our  knowledge 
of  these  forms  is  named  Crystallography,  or  the 
Science  of  Crystals. 

As  our  present  purpose  is  to  enable  a  man  to  de- 
termine his  minerals  in  the  field  and  laboratory  in  the 
quickest  and  shortest  way  consistent  with  a  fair  de- 
gree of  accuracy,  it  would  not  be  necessary  to  devote 
time  to  Crystallography,  if  it  were  not  that  each  min- 
eral tends  to  have  a  more  or  less  distinctive  form  or 
forms;  and  these  forms,  when  sufficiently  perfect  for 
use,  furnish  us  with  the  best,  quickest,  and  surest 
means  of  determining  a  mineral.  In  many  cases  a 
mere  glance  is  sufficient. 


PRELIMINARIES.  3 

A  Mineral,  when  it  shows  its  crystallographic  form, 
is  seen  to  be  bound  by  faces  or  planes;  hence  a  Crystal 
can  be  defined  as  a  body  bounded  by  plane  surfaces.  See 
Fig.  9.  Although  theoretically  the  planes  of  a  crystal  are 
perfect  and  of  equal  size,  yet  in  point  of  fact  this  is  not 
generally  true :  first,  because  of  the  interference  with 
one  another  of  the  adjacent  crystals ;  and  secondly, 
because  of  the  necessity  that  each  one  should  be  im- 
planted or  should  rest  on  something  during  its  process 
of  growth.  By  these  and  other  causes  the  natural 
development  of  the  planes  of  the  crystal  is  hindered, 
and  their  outlines  are  distorted  ;  some  of  the  planes 
may  even  be  totally  suppressed.  Thus  the  crystal 
planes  are  by  no  means  constant  in  outline,  size,  or 
area,  but  they  are  closely,  if  not  entirely,  constant  in 
their  inclination  to  one  another — that  is,  in  the  angles 
that  each  plane  forms  with  those  adjacent  to  it.  See 
Figs.  12-27.  The  variations  of  these  angles  are  so 
slight  that  rarely  can  they  be  detected  except  through 
accurate  instrumental  work.  The  ordinary  work  of  a 
prospector  or  a  student,  who  does  not  desire  to  be  a 
professional  Mineralogist,  but  rather  to  be  able  to  de- 
termine his  minerals  in  the  shortest  way  consistent 
with  a  fair  degree  of  accuracy,  is  such,  that  for  all 
practical  purposes  the  angles  of  any  mineral  species 
may  be  considered  to  be  always  identical. 

Our  method  of  locating  a  point  upon  a  crystal  may 


4  NOTES    ON    CRYSTALLOGRAPHY. 

be  compared  with  the  method  commonly  used  in  locat- 
ing any  point  upon  the  earth's  surface.  In  the  latter 
the  exact  distance  from  a  certain  datum  or  reference 
point  is  determined,  and  the  precise  compass  direction 
obtained.  Thus  one  uses  the  distance  measured  along 
a  certain  line  and  the  angle  which  that  line  makes 
with  the  meridian  of  that  datum  point.  This  is  accur- 
ate enough  for  most  local  purposes  and  becomes  more 
exact  as  one  approaches  the  sea  level.  At  the  sea  level 
one  may  also  measure  a  distance  east  from  a  given 
point,  say  six  miles,  and  then  due  north  to  the  place 
to  be  located  at  a  distance,  say,  of  eight  miles.  It 
could  then  be  stated  that  the  point  sought  lay  eight 
miles  north  and  six  miles  east  of  the  datum  or  refer- 
ence locality.  In  case,  however,  the  point  to  be  located 
is  not  on  the  sea  level,  but  on  high  land  or  a  moun- 
tain, we  would  say  that  the  locality  under  considera- 
tion was  X  miles  south  of  the  datum  or  given  point 
A,  Z  miles  west  of  it,  and  Y  feet  high  above  the  sea 
level.  This  gives  the  exact  position  of  the  point  which 
is  to  be  located  on  the  mountain.  From  this  illustra- 
tion one  can  see  how  points  or  bodies  are  located  in 
space  with  reference  to  a  chosen  point  by  means  of 
three  lines  at  right  angles  to  one  another,  or  by  means 
of  the  same  or  a  greater  number  of  lines  placed  at 
oblique  angles  or  partially  at  right  angles  to  one  an- 
other. 


PRELIMINARIES.  5 

This  system  of  determining  points  can  also  be  used 
for  locating  a  plane  or  any  other  object  in  space,  such 
as  a  star  or  the  plane  of  a  crystal. 

Our  entire  mathematical  conception  of  Crystallog- 
raphy is  based  on  finding  the  location  of  the  crystal 
planes  and  the  angles  they  form  with  one  another 
with  reference  to  a  single  datum  point.  Our  purpose 
in  this  work  is  not  to  discuss  the  subject  mathemati- 
cally, but  merely  to  use  such  mathematical  or  space 
conceptions  as  will  give  us  an  idea  of  the  relative  posi- 
tion of  different  planes  to  the  chosen  datum  point. 

Returning  to  our  idea  of  referring  the  location  of 
any  point  to  three  or  more  lines  and  the  angles  that 
they  make  with  one  another,  we  find  that  there  are 
practically  six  different  methods  or  systems  needed  for 
the  purpose  of  locating  the  different  actual  sets  of 
planes  found  in  nature  upon  the  various  minerals. 

To  apply  these  principles,  first,  select  a  certain 
datum  point  which  is  the  point  forming  the  theoretical 
or  geometrical  centre  of  the  crystals.  This  centre  is 
not  the  actual  centre  of  gravity  of  most  crystals,  but 
the  geometrical  centre  that  would  exist  if  the  crystal 
were  absolutely  perfect,  or  if  we  conceive  the  planes 
so  placed  as  to  make  it  absolutely  faultless.  While 
this  conception  may  appear  difficult  of  attainment, 
yet  with  a  little  attention  and  thought  it  will  be  found 
very  easy  and  simple.  Secondly,  from  the  above 


6  NOTES    ON    CRYSTALLOGRAPHY. 

chosen  point  draw  lines  of  indefinite  length,  which 
form  any  angles  whatsoever  with  one  another,  and  we 
shall,  by  means  of  the  datum  point  and  of  the  three 
or  four  lines  chosen  and  their  angles  of  intersection, 
obtain  data  that  will  enable  us  to  name  the  crystal- 
lographic  forms.  The  above  lines  or  directions  are 
called  Axes. 

The  process  of  learning  to  name  the  forms  is  simple 
and  easy  if  one  employs  care  and  judgment  about  it ; 
and  this  naming  is  all  that  is  required  in  ordinary 
field  and  laboratory  work.  The  mathematical  de- 
scription, calculation  and  correct  drawing  of  the  crys- 
tallographic  forms  is  another  and  much  more  difficult 
matter,  requiring  a  thorough  knowledge  of  the  prin- 
ciples of  Spherical  Trigonometry  or  Analytic  Geom- 
etry of  Three  Dimensions  and  practice  in  Projection 
Drawing.  The  recognition  of  the  crystal  forms  will 
require  on  the  part  of  a  good  student  with  a  suitable 
supply  of  crystal  models  and  natural  crystals  from  15 
to  25  hours  of  study  and  laboratory  practice,  while  the 
mathematical  work  will  demand  months  and  perhaps 
even  years  of  time. 

Our  purpose  in  these  pages  is  simply  to  enable  the 
student  to  study  and  name  the  forms  and  to  under- 
stand the  ordinary  use  of  the  so-called  crystallographic 
nomenclature,  or  the  figures  and  letters  commonly 
written  on  or  about  a  crystal  or  mineral  form,  as  drawn 
and  given  in  our  mineralogical  books  and  papers. 


PRELIMINARIES.  7 

In  representing  our  three  axes  in  a  drawing  (Fig. 
7),  we  readily  see  that  if  three  planes  be  drawn  through 
the  intersection  of  the  lines  at  the  point  A,  and  extend- 
ing along  these  lines,  as  shown  in  Fig.  7,  the  space  is 
then  divided  into  eight  parts  or  Octants ;  for  instance, 
the  part  formed  by  the  planes  meeting  in  the  points 
ABCDEFHisan  octant.  In  an  octant  the 
angles  and  axial  distances  may  all  be  equal,  or  they 
may  all  be  unequal,  or  there  may  be  every  possible 
variation  between  these  limits. 

In  arranging  our  systems  we  start  with  all  the 
angles  in  each  octant  unequal  and  all  the  axes  un- 
equal. In  varying  from  this  we  change  in  each  octant 
first  the  angles,  leaving  the  axes  unequal ;  then  we 
vary  the  axes,  leaving  the  angles  equal.  Our  varia- 
tions of  angles  and  axes  then  are  as  follows : 

1.  Triclinic  System.     All   angles   are  oblique   and 
both  angles  and  axes  unequal.     See  Fig.  1. 

2.  Monoclinic  System.     One  of  the  angles  is  oblique 
and  two  are  right  angles,  but  all  the  axes  are  of  un- 
equal length.     See  Fig.  2. 

3.  Orthorhombic  System.     All  three  angles  are  right 
angles,  but  all  the  axes  remain  unequal.     See  Fig.  3. 

4.  Tetragonal  System.      All  the  angles  are  right 
angles,  but  two  axes  are  equal  and  one  is  unequal  to 
the  other  two.     See  Fig.  4. 

5.  Isometric  System.     All  three  angles  are  equal, 
and  the  three  axes  are  equal.     See  Fig.  5. 


8  NOTES    ON    CRYSTALLOGRAPHY. 

6.  Hexagonal  System.  In  the  sixth  case  we  de- 
part, as  a  matter  of  convenience,  from  the  three  axes 
and  use  four.  Three  of  the  four  axes  are  placed  hori- 
zontally and  form  angles  of  sixty  degrees  with  one 
another.  The  fourth  axis  is  placed  vertically  and 
forms  right  angles  with  the  horizontal  axes.  See 
Fig.  6. 


CHAPTER  II 

THE    TRICLINIC    SYSTEM 

THIS  system  derives  its  name  from  the  Greek  Tris, 
"thrice,"  and  Klino,  "to  slope,  slant,  or  incline 
against,"  the  term  referring  to  the  three-fold  inclina- 
tion of  the  axes  to  one  another.  In  this  system  the 
planes  are  arranged  about  a  given  point  or  theoretical 
centre,  from  which  the  axes  radiate,  all  forming  dif- 
ferent oblique  angles  with  one  another  in  the  same 
octant.  See  Fig.  1.  Practically  the  distance  along 
the  lines  and  the  angles  between  the  lines  are  all  un- 
equal. The  axes  in  Crystallography  are,  however,  no 
more  real  things  than  are  the  poles  of  the  earth,  its 
axis,  equator,  meridians,  or  parallels.  The  axes  are 
simply  chosen  directions  or  imaginary  lines  that  will 
enable  us  to  describe  the  crystal  in  the  shortest  and 
most  convenient  manner.  It  must,  however,  be  re- 
membered that  the  selection  of  the  axes  or  directions 
in  this  system  is  an  arbitrary  thing ;  for  no  matter 
what  directions  may  be  chosen,  still  others  remain 
available. 

(9) 


10  NOTES    ON    CRYSTALLOGRAPHY. 

NOMENCLATURE 

Having  selected  our  axes  and  their  directions,  we 
may  next  define  some  of  the  terms  that  we  must  use 
if  we  desire  to  be.  in  accord  with  other  writers  upon 
this  subject.  If  we  commence  with  any  one  plane 
upon  the  crystal,  that  plane  must  cut  all  three  of  these 
axes  at  some  distance,  or  be  parallel  to  one  or  two  of 
them.  In  accordance  with  geometrical  usage  a  plane 
parallel  to  a  line  is  said  to  cut  that  line  at  infinity,  a 
distance  which,  according  to  mathematical  custom,  is 
designated  by  the  figure  8  laid  upon  its  side  or  hori- 
zontally (  oo  ),  or  by  an  i,  the  initial  of  infinity.  In 
the  Triclinic  System,  when  we  are  studying  a  crystal 
or  model,  the  form  is  so  placed  that  one  axis  is  more 
nearly  vertical  than  the  other  two.  Hence  we  speak 
of  the  first  as  the  Vertical  Axis,  although  such  language 
is  rarely  accurate.  See  Y,  Fig.  1.  The  other  two 
axes  are  called  Lateral  Axes.  See  X  and  Z,  Fig.  1. 

Since  in  this  system  all  the  axes  are  of  unequal 
length  it  is  necessary  to  distinguish  one  lateral  axis 
from  the  other.  This  is  done  by  calling  the  shorter 
axis  the  Brachy-Axis  or  Brachy -Diagonal  (Greek, 
Brachys,  "  short "),  (see  X,  Fig.  1),  and  the  longer  axis 
the  Macro-Axis  or  Macro -Diagonal  (Greek,  Makros, 
"long"),  see  Z,  Fig.  1. 


THE    TRICLINIC    SYSTEM.  11 

PINACOIDS 

In  naming  any  plane  of  a  crystal  in  this  system,  we 
observe  which  one  of  the  three  possible  relations  it 
may  hold  to  the  three  chosen  axes  :  1.  The  plane  may 
intersect  all  three  axes.  2.  It  may  cut  two  axes  and 
be  parallel  to  the  third  axis.  3.  It  may  intersect  one 
axis  and  be  parallel  to  the  other  two.  In  the  last  case 
it  is  evident  that  but  six  such  planes  can  exist  in  this 
system,  each  one  cutting  each  end  of  the  three  axes. 
These  planes  are  called  Finacoids,  from  the  Greek, 
Pinax,  "  a  plank  or  board,"  and  Eidos,  "  shape  or 
form  "  which  in  composition  takes  the  form  of  old  and 
is  translated  "  resembling,  or  like,  or  in  the  form  of." 
The  name  refers  to  the  position  of  each  of  these  planes 
on  the  sides  or  ends  of  the  crystal,  just  as  a  slice  form- 
ing a  plank  or  board  may  be  taken  from  the  side  or 
sides  of  a  mill  log  by  a  saw.  See  010,  Figs.  8-10. 
The  simplest  method  of  designating  the  pinacoids  is 
to  name  them  from  the  axis  that  each  one  cuts ;  but 
practice  has  partially  varied  that  system,  so  that  our 
nomenclature  is  as  follows  : 

1.  If  a  pinacoid  cuts  the  vertical  axis  it  is  called  a 
Vertical  Pinacoid  ;  or  more  commonly,  since  the  crys- 
tals, when  studied,  are  placed  or  allowed  to  rest  on  one 
vertical  pinacoid,  it  is  usually  named  a  Basal  Pinacoid 
or  Basal  Plane.     See  001,  Fig.  33. 

2.  In  case  a  pinacoid  intersects  one  lateral  axis  and 


12  NOTES    ON    CRYSTALLOGRAPHY. 

thus  is  parallel  to  the  other  one  and  the  vertical  axis, 
it  is  named  from  the  lateral  axis  to  which  it  is  parallel. 
If  parallel  to  the  brachy-axis,  it  is  a  Brachy-Pinacoid, 
(see  010,  Figs.  8-10  and  31-35);  if  parallel  to  the 
macro-axis,  it  is  a  Macro-Pinacoid-  See  100,  Figs. 
32-35. 

DOMES  AND  PRISMS 

If  the  plane  cuts  two  axes  but  is  parallel  to  the  third 
axis,  it  is  a  Dome  or  Prism  Plane.  The  term  dome  is 
derived  from  the  Latin  word  domus,  "a  house."  This 
term  is  employed  because,  when  two  dome  planes 
meet,  they  form  an  angle  with  each  other  similar  to 
that  of  the  "  pitch  roof"  of  a  house.  See  110  L  111, 
Figs.  9  and  10.  The  domes  or  dome  planes  are  named 
from  the  axis  to  which  they  are  parallel ;  as,  for  ex- 
ample, a  Brachy-Dome  is  so  named  when  it  lies  par- 
allel to  the  brachy-axis,  (see  021,  Fig.  30,  and  101  and 
102,  Fig.  34) ;  and  a  Macro-Dome  Plane  is  so  called 
when  the  plane  is  parallel  to  the  macro-axis.  Thus 
we  may  call  a  dome,  like  a  house  set  on  end,  parallel 
to  the  vertical  axis,  a  Vertical  Dome  ;  but  it  is  custom- 
ary to  name  the  vertical  dome  planes  Prismatic  Planes, 
and  to  confine  the  term  dome  planes  to  those  planes 
parallel  to  one  of  the  lateral  axes.  See  110,  Figs. 
29-35. 

PYRAMIDS    OR    OCTAHEDRONS 

Having  disposed  of  the  problem  of  naming  two  out 


THE    TRICLINIC    SYSTEM.  13 

of  the  three  possible  series  of  planes  in  this  system,  we 
now  come  to  the  third  or  last  series,  or  the  Pyramids. 
To  repeat,  in  the  first  possible  case  the  planes  might 
intersect  one  axis  and  be  parallel  to  the  other  two, 
giving  rise  to  the  Pinacoidal  Planes;  in  the  second 
possible  series,  the  planes  might  intersect  two  axes  and 
be  parallel  to  the  third,  giving  rise  to  our  Dome  or 
Prism  Planes ;  and  in  this  third  or  last  case,  the  planes 
may  cut  all  three  axes,  forming  Pyramidal  Planes. 
See  111,  Figs.  28-32,  34,  and  35.  These  cases  cover 
all  possible  arrangements  of  planes  about  the  axes  of 
the  Triclinic  System. 

AXIAL    MODELS 

Models  of  the  different  axial  systems  will  be  found 
useful  if  not  indispensable  for  the  proper  understand- 
ing of  the  systems.  These  can  be  made  by  having 
wires  suitably  cut,  and  soldered  together  at  the  proper 
angles ;  or  we  may  thrust  wires  through  cork,  making 
as  before  the  different  systems.  Then,  by  using  a 
piece  of  cardboard  or  better  a  glass  plate  as  a  crystal 
plane  we  can  see  the  relative  position  of  the  planes 
and  the  points  where  they  proportionately  cut  the  axes, 
or  intersect  their  prolongation. 

SIMILAR  AXES,  PLANES,  EDGES,  AND  ANGLES 

In  any  system  of  axes,  one  axis  or  semi-axis  is  con- 
sidered similar  to  another  when  it  has  the  same  length 


14  NOTES    ON    CRYSTALLOGRAPHY. 

and  the  same  inclination  to  the  other  axis  or  semi-axis. 
For  example,  we  may  note  that  in  the  Triclinic  Sys- 
tem none  of  the  semi-axes  are  similar  ;  but  that  in  the 
Isometric  System  all  the  axes  and  semi-axes  are  similar. 
See  Figs.  1-6. 

Planes  are  said  to  be  similar  when  the  distance  from 
the  centre  to  the  points  at  which  they  cut  similar 
semi-axes  are  equal.  See  planes  111,  111,  111  and 
111,  Figs.  12,  15,  17,  and  18. 

One  edge  is  said  to  be  similar  to  another  edge  when 
both  are  formed  by  the  intersection  of  two  similar 
planes.  See  the  octahedral  edges  in  Fig.  12. 

A  solid  or  crystal  angle  is  said  to  be  similar  to  an- 
other crystal   angle  when   both    are    formed   by  the 
same  number  of  similar  planes.     See  the  octahedral 
solid  angles  in  Fig.  1 2. 
j 

SYMMETRY 

The  question  naturally  arising  first  in  the  mind  of 
any  student  is  how  he  can  ascertain  whether  the  crys- 
tal or  crystal  model  belongs  to  the  Triclinic  System 
or  not.  In  order  to  make  this  fairly  easy,  attention  is 
called  here  to  symmetry.  The  meaning  of  symmetry 
as  here  used  may  be  illustrated  by  reference  to  a  well- 
proportioned  or  symmetrical  man.  In  this  case  his 
right  hand  is  similar  to  his  left  hand,  and  his  right 
ear,  eye,  arm,  leg,  and  foot  will  also  be  similar  when 


THE    TRICLINIC    SYSTEM.  15 

each  is  compared  with  the  corresponding  member  on 
the  left  side  of  the  body.  The  same  illustration  can 
be  carried  out  if  we  take  certain  undivided  parts  of 
the  body,  as  for  instance,  the  nose.  A  plane  exactly 
cutting  the  nose  from  top  to  bottom  into  two  equal 
parts  would  have  the  right  nostril  similar  to  the  left, 
i.  e.,  the  right  half  of  the  nose  would  be  similar  to  the 
left  half.  A  like  division  of  the  mouth  and  tongue 
would  show  that  the  two  parts  of  each  are  similar.  If 
we  undertake  to  divide  the  body  of  a  man  into  two 
equal  parts  so  that  each  half  shall  be  symmetrical  with 
the  other  half,  a  little  observation  and  thought  will 
show  us  that  there  is  only  one  position  in  which  such 
a  plane  can  be  passed  directly  through  the  body  ;  e.  g., 
from  the  head  to  the  feet,  separating  the  skull,  nose, 
mouth,  thorax,  etc.,  into  two  equal  and  symmetrical 
parts.  The  same  thing  can  be  done  with  many  other 
animals,  like  the  dog  or  cat.  The  symmetry  in  such 
cases  is  said  to  be  bilateral,  and  the  plane  that  will 
divide  the  object  into  two  symmetrical  halves  is  called 
a  Plane  of  Symmetry.  See  plane  ABCD,  Fig.  9. 

In  the  majority  of  the  lower  orders  of  animals  and 
plants  more  than  one  plane — sometimes  several,  some- 
times many — can  be  found  that  will  divide  the  object 
into  two  equal  and  symmetrical  parts.  So,  too,  in 
our  crystals,  the  number  of  planes  of  symmetry  may 
vary  in  the  different  systems  from  none  to  nine  ;  and 


16  NOTES    ON    CRYSTALLOGRAPHY. 

in  some  cases  they  are  extremely  important  as  dis- 
tinguishing characteristics  of  the  systems.  Symmetry 
does  not  exist  in  the  abnormal  and  distorted  forms  of 
man  or  of  other  animals  or  of  minerals,  although  the 
normal  forms  may  show  perfect  or  approximately  per- 
fect symmetry. 

It  is  a  common  mistake  for  a  student  to  suppose 
that  symmetry  implies  that  qne  of  the  symmetrical 
halves  can  exactly  replace  the  other  half.  This  is  not 
a  requirement  of  symmetry..  The  left  half  of  a  man 
can  not  be  put  in  the  position  of  the  right  half  and  fill 
its  place ;  the  necessary  requirement  is  that  the  oppo- 
site halves  shall  have  the  same  members  and  be  simi- 
lar in  form.  In  crystals  it  is  requisite  that  the  planes, 
edges,  and  angles  should  be  similar  for  each  half. 

Again,  it  is  necessary  that  the  two  halves  be  sym- 
metrical when  looked  at  from  any  position,  so  that  the 
plane  of  symmetry,  if  prolonged,  would  bisect  the  nose, 
eyes,  and  mouth  of  the  observer ;  yet  there  is  no  more 
common  mistake  on  the  part  of  the  inexperienced 
student  than  to  think  that  a  crystal  is  symmetrical,  if 
after  bisecting  it  with  a  plane  of  symmetry,  he  can 
turn  one  half  into  some  other  position  so  that  it  will 
then  stand  symmetrical  with  the  other  half.  The 
symmetry  must  show  without  any  turning  or  twisting 
of  the  crystal.  Certainly  no  one  would  ever  think  of 
making  the  two  halves  of  a  man  symmetrical  by  turn- 


THE    TRICLINIC    SYSTEM.  17 

ing  one-half  partly  around  ;  and,  while  not  as  obvious 
to  the  observer,  it  is  equally  absurd  to  turn  one-half  of 
the  crystal  partly  around  to  make  it  symmetrical  with 
the  other  half. 

If  ordinary  observation  will  not  determine  for  the 
student  a  plane  of  symmetry,  he  can  ascertain  whether 
or  not  any  chosen  plane  is  a  plane  of  symmetry  by 
holding  the  crystal  or  model  in  front  of  a  mirror,  with 
the  supposed  plane  of  symmetry  exactly  parallel  to  the 
face  of  the  mirror.  If  then  the  reflection  of  the  side 
of  the  crystal  or  model  shown  in  the  mirror  is  exactly 
like  the  side  of  the  crystal  next  to  the  observer  or 
farthest  from  the  mirror,  the  plane  in  question  is  a 
plane  of  symmetry. 

If  we  examine  Figs.  8—11,  we  can  see  what  a  plane 
of  symmetry  means  in  those  forms.  In  Figs.  8  and  9 
the  plane  of  symmetry  is  the  plane  formed  by  the 
rhomboid  A  B  C  D.  In  these  figures  it  can  be  seen 
that  this  plane  so  divides  the  crystals  that  the  planes 
e,  f  and  P  on  one  side  are  exactly  matched  by  sim- 
ilar planes  on  the  other  side  of  the  crystal.  In  Fig. 
10  the  six-sided  plane  A  B  C  D  H  is  the  plane  of 
symmetry,  and  it  divides  the  crystal  into  two  similar 
halves,  in  which  the  right-hand  plane  /  matches  the 
left-hand  plane  /,  and  so  on.  In  the  case  of  Fig.  11 
the  plane  of  symmetry  is  the  rhomboid  A  B  C  D, 
which  divides  the  plane  r  into  two  equal  parts,  and 
'  2 


18  NOTES    ON    CRYSTALLOGRAPHY. 

has  the  right  side  planes,  I  and  ^/matched  by  similar 
planes  on  the  left  side. 

Symmetry  shows  itself  not  only  in  planes  of  sym- 
metry but  also  in  Axes  and  in  Centres  of  Symmetry. 
When  any  direction  is  selected  as  an  axis  and  the 
crystal  or  model  is  revolved  about  that  axis,  if  similar 
planes  or  angles  show  from  tyne  to  time  in  the  same 
position  on  the  form  during  such  revolutions,  the 
selected  direction  is  called  an  Axis  of  Symmetry. 

If  the  crystals  represented  by  Figs.  36—40  are  re- 
volved about  the  vertical  axis,  it  will  be  noticed  that 
in  each  case  similar  planes  are  presented  six  times  to 
the  observer.  Because  the  same  faces  recur  six  times 
during  one  complete  revolution,  such  an  axis  of  sym- 
metry is  called  an  Axis  of  Hexagonal  Symmetry 
(Greek,  Hex,  "  six  "  and  Gonos,  "  angle  "). 

In  the  case  of  Figs.  8-11,  a  like  revolution  of  the 
crystals,  which  they  represent,  about  their  vertical  axis 
shows  the  recurrence  of  similar  faces  in  but  two  posi- 
tions ;  hence  this  symmetry  is  called  an  Axis  of  Binary 
Symmetry  (Latin,  Binarius,  "  consisting  of  two  "). 

In  Figs.  41-44,  a  similar  revolution  of  the  crystals, 
which  they  represent,  would  show  four  positions  in 
which  similar  faces  present  themselves.  This  axis  of 
symmetry  is  then  an  Axis  of  Tetragonal  Symmetry 
(Greek,  Tetra,  "four"). 

Figs.  45-50  show,  when  the  crystals  they  represent 


THE    TRICLINIC    SYSTEM.  19 

are  revolved  about  the  vertical  axis,  an  Axis  of  Trig- 
onal Symmetry  (Greek,  Tris,  "  thrice  "). 

Crystals  can  have  only  Axes  of  Binary,  Trigonal, 
Tetragonal,  and  Hexagonal  Symmetry. 

When  each  face,  angle,  and  edge  of  a  crystal  or 
crystal  model  has  a  similar  face,  angle,  or  edge  re- 
peated exactly  on  the  opposite  side  of  the  crystal  or 
model,  the  theoretical  central  point  or  axial  centre  of 
the  crystal  or  model  is  a  Centre  of  Symmetry.  Or,  in 
other  words,  whenever  one-half  of  the  crystal  or  model 
has  every  plane,  angle,  and  edge  repeated  by  a  similar 
plane,  angle,  or  edge  on  the  opposite  half,  the  centre 
of  that  form  is  a  Centre  of  Symmetry.  Thus  Centres 
of  Symmetry  are  shown  in  Figs.  28-35,  as  the  centre 
of  each  crystal  has  on  one  side  a  face  matched  by  a 
plane  on  the  other  side ;  the  same  fact  can  be  noted 
concerning  all  the  other  faces,  angles,  and  edges  on 
the  crystals  which  these  figures  represent. 

DISTINGUISHING     CHARACTERISTICS     OF     THE     TRICLINIC 
CRYSTALS 

It  is  hardly  scientific  to  define  anything  by  stating 
what  it  has  not,  but  in  many  cases  this  method  of  de- 
scription is  the  simplest.  So  here  we  may  say  that 
the  Triclinic  System  is  characterized  by  the  fact  that 
it  has  no  plane  of  symmetry  ;  that  is,  we  can  find,  in 
crystals  belonging  to  this  system,  no  plane  that  will 


20  NOTES    ON    CRYSTALLOGRAPHY. 

divide  the  crystals  into  two  equal  and  symmetrical 
parts.  See  Figs.  28-35. 

The  absence  of  any  plane  of  symmetry,  while  char- 
acteristic of  the  Triclinic  System,  is  not  an  absolute 
proof  of  it,  since  some  of  the  forms  in  the  other  sys- 
tems have  also  no  plane  of  symmetry.  These  forms 
are  so  extremely  rare  in  the  case  of  minerals  that  they 
will  occasion  no  trouble  in  the  field,  and  it  is  only  in 
the  case  of  crystal  models  or  in  artificial  crystals  that 
any  difficulty  will  occur. 

All  difficulties,  however,  will  disappear  if  we  re- 
member that  in  the  case  of  the  other  five  systems  all 
the  forms  that  have  no  plane  of  symmetry  do  have 
one  or  more  axes  of  symmetry,  while  all  the  Triclinic 
forms  are  destitute  of  any  axis  of  symmetry  as  well  as 
of  any  planes  of  symmetry.  They  can  only  have  a 
centre  of  symmetry. 

Again,  if  a  Triclinic  crystal  is  placed  on  its  basal 
plane,  it  can  readily  be  seen  that  the  side  planes  form 
oblique  angles  with  the  basal  plane.  In  fact,  the 
obliquity  of  the  planes  to  one  another  or  the  twisting 
of  the  forms,  as  if  a  box  were  taken  by  its  corners  and 
twisted  out  of  shape,  can  usually  be  seen  in  whatever 
position  the  crystals  are  placed. 

From  the  obliquity  of  the  angles  the  crystals  of  the 
Triclinic  System  are  quite  apt  to  have  wedge-shaped 
forms,  although  the  wedges  are  twisted  or  skewed,  and 


THE    TRICLINIC    SYSTEM.  21 

not  straight,  as  are  the  wedge-shaped  forms  in  the 
other  systems.     See  Figs.  28-35. 
From  the  above  characters  : 

1.  Determine  whether  or  not  the  crystal  model  be- 
longs to  the  Triclinic  System. 

2.  Determine  where  the  three  axes  are  to  be  placed. 
They  must  be  so  located  as  to  fulfill  the  requirements 
of  this  system ;  that  is,  they  must  be  of  equal  length 
and  form  oblique  angles  with  one  another.     If  these 
conditions  are  fulfilled,  then  it  is  best  to  locate  each 
axis  parallel  to  some  plane  or  edge  :  the  planes  or 
edges  chosen  must  hold    the    same   relation   to  one 
another ;  i.  e.,  they  must  form  oblique  angles  and  be 
of  unequal  length.     As  a  rule  place  the  axes  so  as  to 
have  first,  as  many  pinacoidal  planes  as  possible,  and 
next  as  many  prism  or  dome  planes  as  possible,  but 
with  the  fewest  possible  pyramidal  planes. 

RULES    FOR    NAMING    TRICLINIC    PLANES 

I.  If  any  plane  cuts  one  axis  and  is  parallel  to  the 
other  two,  it  is  a  Pinacoid.     If  it  cuts  the  vertical  axis, 
it  is  a  Basal  or  Vertical  Pinacoid,  or  a  Basal  Plane ; 
if  it  intersects  the  brachy-axis,  it  is  a  Macro -Pinacoid ; 
if  it  cuts  the  macro-axis,  it  is  a  Brachy-Pinacoid. 

II.  If  any  plane  cuts  two  axes  and  is  parallel  to  the 
third  axis,  it  is  a  Dome  or  Prism  Plane,  and  is  named 
from  the  axis  to  which  it  is  parallel :  if  it  is  parallel  to 


22  NOTES    ON    CRYSTALLOGRAPHY. 

the  vertical  axis,  it  is  a  Prism  or  a  Vertical- Dome 
Plane ;  if  it  is  parallel  to  the  brachy-axis,  it  is  a 
Brachy-Dome  Plane ;  if  it  is  parallel  to  the  macro-axis, 
it  is  a  Macro-Dome  Plane. 

III.  If  a  plane  cut  all  three  axes,  it  is  a  Pyramidal 
or  Octahedral  Plane. 

FORMS 

The  term  Form  is  employed  in  Crystallography  to 
indicate  the  union  of  similar  planes  about  crystallog- 
raphic  axes. 

These  planes  may  or  may  not  inclose  space.  In  the 
case  of  eight  similar  planes  forming  an  octahedron, 
space  is  inclosed  between  the  planes.  Four  similar 
dome  planes,  arranged  parallel  to  the  same  axis, 
inclose  space  in  the  same  way  that  a  stove-pipe 
does,  but  the  ends  are  open,  and  space  can  only 
be  actually  inclosed  by  the  addition  of  two  pinacoids, 
one  at  each  end.  In  like  manner,  two  pinacoids  in 
the  Tetragonal  or  Hexagonal  Systems  make  a  form, 
but  they  do  not  inclose  space. 

From  the  above,  we  can  see  that  in  Crystallography 
the  term  form  frequently  has  a  significance  somewhat 
different  from  its  ordinary  meaning. 

In  Crystallography  we  have  complete  forms,  half 
forms,  and  quarter  forms ;  and  to  enable  us  better  to 
understand  the  meaning  of  forms  in  Crystallography, 
it  is  necessary  to  define  these  three  kinds  of  forms. 


THE    TRICLINIC    SYSTEM.  23 

1.  Holohedral  Forms  occur  when  we  have  a  union  of 
all  the  similar  possible  planes  that  can  be  arranged 
about  the  axes  of  any  crystallographic  system.  See 
Fig.  12.  The  name  comes  from  the  combination  of  two 
Greek  words,  Holos,  "  whole,  perfect  or  complete,"  and 
Hedra,  "  a  seat  of  any  kind  like  a  chair,  stool  or  bench, 
or  a  foundation  or  base."  This  makes  a  somewhat  far- 
fetched translation,  as  the  implication  is  that  the  seats 
or  places  are  all  filled,  which  in  Crystallography  is 
said  to  mean  a  form  with  all  possible  faces.  When 
crystals  have  the  entire  number  of  similar  possible 
faces,  it  is  customary  to  call  them  Holohedral  Forms  ; 
and  it  should  be  noted  that  these  forms  possess  all  the 
symmetry  possible  in  any  given  crystallographic  sys- 
tem ;  i.  e.j  they  have  all  the  planes,  axes,  and  centres 
of  symmetry  possible  in  that  system.  Such  crystals 
are  said  to  have  the  highest  symmetry.  It  should  be 
noted  that  the  highest  symmetry  in  the  Isometric 
System  comprises  nine  planes  of  symmetry,  three  axes 
of  tetragonal  symmetry,  four  axes  of  trigonal  sym- 
metry, six  axes  of  binary  symmetry,  and  a  centre  of 
symmetry.  See  Figs.  12,  15,  and  17.  Again,  the 
highest  symmetry  of  the  Orthorhombic  System  is 
expressed  by  three  planes  of  symmetry,  three  axes  of 
binary  symmetry,  and  a  centre  of  symmetry.  See 
Fig.  51. 

Further,  the  Triclinic  System  has  no  plane  or  axis  of 


24  NOTES    ON    CRYSTALLOGRAPHY. 

symmetry,  but  only  a  centre  of  symmetry.  See  Figs. 
28-35.  When  the  subject  of  Crystallography  is  devel- 
oped from  the  Isometric  System  and  ends  with  the  Tri- 
clinic,  it  begins  with  the  highest  possible  symmetry  and 
complexity,  descending  towards  the  lower  and  simpler 
forms.  On  the  other  hand,  if  the  development  begins 
with  the  Triclinic  System,  it  commences  with  the 
simplest  forms,  or  lowest  symmetry,  and  ascends 
towards  the  highest  and  most  complex  forms. 

2.  Hemihedral  Forms  occur  when  we  have  a  union 
of  one-half  of  all  the  similar  possible  planes  that  can 
be  arranged  about  the  axes  of  any  crystallographic 
system.  Hence  all  such  forms  are  called  hemi-forms, 
from  the  Greek,  Hemisys,  "  the  half,"  which  is  ordi- 
narily contracted  in  compound  words  to  Hemi  or 
"  half." 

In  the  Hemihedral  Forms  the  symmetry  is  lower 
than  in  the  Holohedral  Forms  ;  i.  e.,  there  are  fewer 
planes  or  axes  of  symmetry  than  in  the  Holohedral 
Forms.  For  example,  one  set  of  Hemihedral  Forms 
in  the  Isometric  System  has  three  planes  of  symmetry, 
four  axes  of  trigonal  symmetry,  three  axes  of  binary 
symmetry,  and  a  centre  of  symmetry.  See  Figs.  52 
and  53. 

In  the  Triclinic  System  it  should  be  noticed  that  at 
the  most  only  two  planes  in  any  case  are  alike,  i.  e., 
have  similar  indices.  So  in  the  case  of  the  Prisms 


THE    TRICLINIC    SYSTEM.  25 

and  Domes,  instead  of  four  similar  sides,  there  exist 
only  two,  or  one-half  of  the  completed  form  ;  hence 
these  forms  are  called  Henri-Prisms  and  Hemi-Domes. 

3.  Tetartohedral  Forms  occur  when  we  have  a  union 
of  one-fourth  of  all  the  similar  possible  planes  that  can 
be  arranged  about  the  axes  of  any  crystallographic 
system.  These  forms  are  called  Tetartohedral  Forms, 
from  the  Greek,  Tetartos,  "the  fourth  part  of  any 
thing."  In  the  Triclinic  System  the  Pyramids  or 
Octahedrons  have  only  one  quarter  of  the  faces  neces- 
sary to  make  a  complete  form  ;  hence,  instead  of  call- 
ing the  faces  Pyramids,  it  is  correct  to  speak  of  them 
as  Tetarto-Pyramids.  See  Figs.  28-32  and  111,  Figs. 
34  and  35. 

The  Tetartohedral  Forms  have  a  low  order  of 
symmetry,  as  shown  in  the  planes,  axes,  or  centres  of 
symmetry  ;  for  example,  in  the  Hexagonal  System  a 
tetartohedral  form  known  as  the  Trigonal  Trapezo- 
hedron  has  neither  plane  nor  centre  of  symmetry,  but 
has  one  axis  of  trigonal  and  three  axes  of  binary  sym- 
metry. See  Figs.  54  and  55. 

SIMPLE  AND  COMPOUND  CRYSTALS 

A  crystal  is  said  to  be  simple  when  it  is  made  up  of 
the  planes  of  one  form  only.  See  Figs.  7,  12,  and 
52-55  ;  but  it  is  called  compound  when  it  is  com- 
posed of  the  planes  of  two  or  more  different  forms. 


26  NOTES    ON    CRYSTALLOGRAPHY. 

See  Figs.  8-11,  15-18,  and  28-51.  Compound  crys- 
tals comprise  a  large  majority  of  crystals.  Simple 
crystals  are  found  in  the  Hexagonal  and  Isometric 
Systems  more  often  than  in  any  of  the  others ;  while 
the  Triclinic  and  Monoclinic  crystals  are  all  com- 
pound, for  no  single  form  in  these  systems  can  inclose 
space.  See  Figs.  28  and  35. 

In  describing  these  forms  we  require  some  special 
terms.  Occasionally  the  planes  of  the  several  forms 
that  make  the  compound  crystals  are  all  equally  de- 
veloped ;  but  in  most  cases  the  planes  of  one  form  are 
more  conspicuous  than  are  those  of  the  others.  The 
chief  form  is  called  the  Dominant  Form  and  second- 
ary ones  are  called  Subordinate  Forms.  See  Fig.  17. 

In  describing  a  crystal  or  model,  it  is  usual  to  select 
the  most  conspicuous  form  as  the  Dominant  Form,  and 
then  to  state  that  it  is  modified  by  such  and  such 
Subordinate  Forms,  naming  the  secondary  forms  one 
after  the  other,  in  the  order  of  their  prominence.  For 
example,  in  Fig.  17  we  say  that  the  dominant  form  is 
an  octahedron  (111)  modified,  first,  by  the  planes  of  a 
cube,  (100),  and,  secondly,  by  the  planes  of  a  dodeca- 
hedron, (110). 

In  the  union  of  the  various  forms  that  make  up  the 
completed  crystal,  the  planes  of  one  form  take  the 
place  of  the  edges  or  solid  angles  of  another  form.  In 
such  a  case  we  use  the  term  Replace  to  indicate  the  re- 


THE    TRICLINIC    SYSTEM.  27 

lation  of  the  two  forms.  For  example,  in  Fig.  17  the 
dominant  form  is  an  octahedron  (111),  the  solid  angles 
of  which  are  replaced  by  the  planes  of  a  cube  (100),  and 
the  edges  of  which  are  replaced  by  the  planes  of  a  do- 
decahedron (110).  In  the  above  example  the  dodeca- 
hedral  planes,  (110),  make,  on  each  of  their  sides,  equal 
angles  with  the  octahedral  planes  (111);  in  such  cases  we 
commonly  say  that  the  edge  of  the  octahedron  (111)  has 
been  truncated.  In  like  manner,  the  cube  plane  (100)  is 
equally  inclined  to  the  four  adjacent  faces  of  the  octa- 
hedron (111).  In  this  case  we  usually  say  that  the  solid 
angles  of  the  octahedron  (111)  have  been  truncated  by 
the  planes  of  a  cube  (100).  From  this  we  may  define 
Truncation  of  an  edge  as  the  Replacement  of  that  edge 
by  a  plane  equally  inclined  to  the  adjacent  similar 
planes.  The  Truncation  of  a  solid  angle  is  the  Replace- 
ment of  that  angle  by  a  plane  equally  inclined  to  the 
adjacent  similar  planes.  Figs.  56-58  show  a  form  of 
replacement  that  is  commonly  distinguished  by  the 
special  term  Bevelment.  In  this  we  can  see  that  the 
two  repla-cing  planes  are  unequally  inclined  on  oppo- 
site sides  to  the  two  planes  forming  the  replaced  edge, 
but  that  the  intersections  of  all  the  planes  are  parallel. 
In  Fig.  58  the  replaced  edge  was  formed  by  the  meeting 
of  the  two  planes,  a  and  d.  This  edge  is  now  replaced 
by  the  planes  b  (310)  and  c  (130).  The  plane  6,  for  in- 
stance, inclines  on  the  plane  a  (100)  at  the  same  angle 


28  NOTES    ON    CRYSTALLOGRAPHY. 

that  the  plane  c  does  on  the  cube  face  d  (010).  Again, 
the  plane  b  inclines  to  the  cube  face  d  at  a  different  angle 
from  its  inclination  upon  the  cube  face  a.  The  plane  c, 
in  like  manner,  inclines  on  the  cube  face  a  at  a  different 
angle  from  that  which  it  makes  on  c.  These  opposite 
inclinations  are  equal  in  the  two  planes.  If  this  were 
not  so,  the  intersections  could  not  be  parallel.  We 
say  then  that  an  edge  is  Bevelled  when  it  is  replaced 
by  two  planes  which  are  unequally  inclined  on  oppo- 
site sides  to  the  two  planes  forming  the  replaced  edge, 
but  which  have  all  their  intersections  parallel. 

It  needs  to  be  noted  that  in  studying  a  crystal  com- 
posed of  several  forms,  no  attention  is  to  be  paid  to 
the  shape  or  size  of  the  replacing  planes.  Their  in- 
clinations to  the  axes  are  the  only  points  with  which 
we  are  concerned. 

READING    CRYSTALLOGRAPHIC    DRAWINGS 

In  order  to  express  the  relations  of  the  different 
planes  to  one  another  upon  a  crystal  and  to  enable 
one  crystallographer  to  understand  the  work  of  an- 
other, without  his  writing  out  long  and  tedious  de- 
scriptions, several  systems  of  crystallographic  short- 
hand have  been  proposed.  Of  these  systems,  the  one 
that  formerly  prevailed  amongst  English-speaking 
people  is  the  German  system  of  Weiss,  which  was 
subsequently  modified  by  Naumann,  and  later  by 


THE    TRICLINIC    SYSTEM.  29 

J.  D.  Dana,  whose  symbols  are  the  simplest  of  the 
three.  The  present  prevailing  system  of  notation,  or 
at  least  the  one  that  will  in  time  receive  almost  if  not 
quite  universal  adoption,  is  the  Whewell-Grassmann- 
Miller  system  as  modified  by  Bravais.  For  the  ele- 
mentary conception  of  crystals  the  crystallographic 
system  of  Naumann  is  more  easily  understood  by  the 
student  and  is  better  from  the  observational  stand- 
point ;  but  for  the  work  of  the  crystallographer  the 
Miller  notation  or  the  Miller-Bravais  system  lends 
itself  to  easier  calculations,  and  is  superior  from  the 
the  mathematical  view-point. 

The  French  have  generally  employed  the  Haiiy 
notation  as  modified  by  Le>y  and  Des  Cloizeaux,  but 
for  our  purpose  attention  will  be  given  only  to  the 
notations  of  Weiss,  Naumann,  Dana  arid  Miller- 
Bravais.  These  notations  have  been  modified  by 
some  later  cry  stall  ographers,  notably  Groth. 

It  is  now  time  to  turn  our  attention  to  crystallo- 
graphic symbols.  The  first  to  be  considered  are  those 
belonging  to  the  axial  notations.  See  Fig.  1.  In 
this  system,  where  the  three  axes  are  all  of  different 
lengths,  the  shorter  lateral  semi-axis  is  designated  by 
the  italic  letter  a,  over  which  the  printer's  breve  or 
short  vowel  mark  (— )  is  placed  to  indicate  that  it  is  the 
shorter  lateral  semi-axis  or  brachy-semi-axis.  In  a 
similar  manner  the  longer  of  the  lateral  semi-axes  is 


30  NOTES    ON    CRYSTALLOGRAPHY. 

designated  by  the  italic  letter  b,  over  which  the  macron 
or  printer's  long  vowel  mark  (-)  is  placed  to  indicate 
that  this  is  the  longer  lateral  semi-axis  or  macro- 
semi-axis. 

The  vertical  semi-axis  is  designated  by  the  italic 
letter  c,  over  which  is  erected  a  short  vertical  mark  or 
perpendicular  (  •  )  to  indicate  that  this  refers  to  the 
vertical  semi-axis. 

A  plane,  in  crystallographic  notation,  is  always 
designated  by  the  distance  from  the  centre  to  the 
point  at  which  it  intersects  each  axis.  The  beginner 
may  think  this  a  very  difficult  procedure,  but  in  prac- 
tice it  is  simple  enough  ;  for  we  deal  only  with  the 
relative  distances  and  have  nothing  at  all  to  do  with 
the  absolute  distances.  If  the  axes  are  different,  as 
they  are  in  this  system,  we  assume  a  unit  of  distance 
on  each  axis :  the  unit  is  not  an  inch  or  any  other 
standard  measure  of  length,  but  implies  that  if  one 
plane  cut  the  axis  at  unity  or  1,  another  plane  may 
also  intersect  this  axis  at  f ,  j,  2,  3,  4,  or  any  number 
of  times  that  unit  of  distance. 

If  we  had  hundreds  of  crystal  planes  parallel  to  one 
another,  they  could  all  then  be  reduced  to  our  unit  of 
distance  and  thus  considered  as  one.  It  is  only  when 
the  planes  vary  in  their  intercepts  upon  the  axes  that 
they  are  considered  as  separate  planes.  If  in  any 
crystal  a  plane  is  selected  as  the  standard,  it  will  be 


THE    TRICLINIC    SYSTEM.  31 

found  that  all  other  planes  intercept  the  axes  either 
with  the  same  unit  of  distance  or  at  some  simple  mul- 
tiple or  fraction  of  it,  like  J,  J,  J,  },  f,  |,  f,  2,  3,  4,  5, 
6,  7,  8,  9,  and  so  on. 

The  intercepts  of  a  plane  upon  the  axes  are  known 
as  the  Parameters ;  or  we  may  define  the  parameters 
as  the  relative  distances  from  the  chosen  centre  of  the 
crystal  to  the  point  at  which  a  plane  intersects  the 
the  imaginary  axes.  The  important  thing  about  a 
crystal  plane  is  its  inclination  to  the  axes.  This  in- 
clination varies  only  when  the  parameters  vary ;  for 
if  the  parameters  of  one  plane  are  written  1  a  :  3  b  : 
2  c  and  those  of  another  plane  written  4  a  :  12  b  :  8  c, 
it  becomes  at  once  apparent  that  if  we  divide  the 
second  set  of  parameters  by  4,  they  reduce  to  the  same 
form  as  the  first,  and  that  therefore  the  inclinations  of 
the  two  planes  are  identical  and  the  planes  are  both 
the  same.  From  this  it  follows  that  the  parameters 
should  always  be  reduced  to  their  lowest  terms  or  have 
no  common  divisor.  It  may  further  be  noticed  that 
the  sizes  of  the  planes  have  no  significance  in  Crystal- 
lography. 

To  return  to  our  laws  for  the  nomenclature  of  planes 
in  the  Triclinic  System  :  by  noting  the  position  where 
the  Vertical  Pinacoid  or  Basal  Plane  cuts  each  axis, 
and  by  writing  the  axes  with  the  parameter  figures,  we 
can  see  at  once  that  the  parameters  of  this  plane  will 


32  NOTES    ON    CRYSTALLOGRAPHY. 

be  as  follows :  oo  a  :  co  6  :  1  c.  Now  the  figure  1  be- 
fore the  c  is  superfluous,  and  the  parameters  can  be 
written  thus :  oo  a  :  oo  b  :  c.  These  symbols  may  be 
translated  as  follows :  the  plane  in  question  cuts  both 
lateral  axes  at  infinity  or  is  parallel  to  them,  while  it 
intersects  the  vertical  axis  at  the  unit  of  distance. 
Such  a  plane  can  only  be  a  Vertical  Pinacoid  or  Basal 
Plane.  When  the  parameters  are  written  as  above, 
the  notation  is  known  as  the  Weiss  system.  Naumann 
abbreviated  this  form  by  writing  the  capital  letter  P 
and  placing  zero  before  it,  as  follows :  0  P.  Dana 
further  abbreviated  by  writing  this  plane  as  0  or  c. 
Miller  employs  the  reciprocals  of  the  Weiss  param- 
eters, calling  them  Indices;  e.  g.,  in  the  above,  the 
reciprocals  are  ^  :  <£  :  -J-  =  0  :  0  :  1  ;  or,  as  it  is  the 
custom  to  write  the  indices  in  the  Miller  system  with- 
out colons,  the  indices  are  written  as  follows :  0  0  1. 

In  every  case  in  the  Miller  system  where  any  of  the 
reciprocals  are  in  the  form  of  fractions,  all  the  indices 
are  multiplied  by  the  smallest  number  that  will  re- 
duce all  these  fractions  to  whole  numbers.  From  this 
it  follows  that  all  the  Miller  indices  are  whole  num- 
bers, generally  ranging  from  0  to  6. 

In  following  out  the  above  notations  our  symbols 
for  the  Brachy- Pinacoid  would  be  in  the  Weiss 
method  :  oo  a  :  b  :  co  c,  modified  by  Naumann  to 
QO  P  co  ,  or  oo  P  GO  ,  and  by  Dana  to  i-i,  or  a.  Miller's 
indices  would  be  0  1  0. 


THE    TRICLINIC    SYSTEM.  33 

In  the  case  of  a  prismatic  plane  the  Weiss  notation 
would  be  a  :  b  :  oo  c,  or  a  :  -b  :  GO  c,  according  as  the 
plane  cuts  the  axis  b  (Fig.  1)  on  the  right  or  the  left 
side.  Naumann's  modifications  are  as  follows  :  oo  P 
for  the  first,  and  oo  'P  for  the  second.  Both  of  these 
Dana  abbreviates  as  I'  or  m,  and  v/6r  M.* 

In  marking  the  directions  on  the  axes,  parameters 
taken  on  the  lateral  axes  to  the  front  and  to  the  right 
side  are  considered  positive,  but  those  measured  to- 
wards the  back  and  to  the  left  side  are  called  negative. 
The  direction  taken  on  the  vertical  axis  above  the 
lateral  axes  is  called  positive,  while  that  below  is 
called  negative.  See  Fig.  1. 

The  positive  sign  (+)  is  not  usually  given,  for  it  is 
understood  that  unless  the  negative  ( — )  sign  is  written, 
all  the  parameters  are  positive.  In  order  to  indicate 
the  different  positions  relative  to  the  axes,  Naumann 
used  the  accent  mark  placed  to  the  right  or  left  above 
and  to  the  right  or  left  below,  as  follows  :  P,  'P,  P,,  ,P. 
See  Fig.  28.  Some  employ  the  accent  mark  not  about 
the  P,  but  in  the  same  relative  position  about  the  let- 
ters or  infinity  sign  accompanying  the  P;  as  raP  oo  ', 
or  /fmP  oo  . 

*  Besides  using  the  symbols  of  Naumann,  Dana,  or  Miller  to  desig- 
nate the  planes  upon  a  crystal,  it  is  not  uncommon  to  select  letters  with 
or  without  any  system.  In  such  instances  the  text  is  expected  to  ex- 
plain the  notation  in  each  case.  Figs.  28-35  illustrate  some  of  the 
methods  of  notation  in  the  Triclinic  System. 

3 


34  NOTES   ON   CRYSTALLOGRAPHY. 

In  the  Miller  notation  as  now  employed  the  a  semi- 
axis  is  always  given  first,  the  b  semi-axis  second,  and 
the  c  semi-axis  third,  using  for  the  indices  either 
known  integers,  or  else  employing  in  their  places  the 
letters  h  for  the  a  semi-axis,  k  for  the  b  semi-axis,  and 
I  for  the  c  semi-axis.  But  whenever  either  the  h,  k, 
or  I  become  equal  in  value  to  one  of  the  others,  then 
the  same  letter  is  used  in  both  cases ;  as,  h  h  I,  or  h 
k  k.  When  all  three  letters  have  the  same  values,  the 
indices  reduce  instantly  from  h  h  h  to  1  1  1.  When- 
ever the  direction  is  taken  negatively  in  the  Miller 
indices,  the  negative  sign  is  written  above  the  letter, 
as  h. 

If  the  student  now  understands  the  Weiss  system  of 
notation  derived  from  the  intercepts  of  each  plane 
upon  each  axis,  it  is  hoped  that  Figs.  28-35  and  the 
following  table  adapted  from  the  works  of  Bauerman, 
J.  D.  and  E.  S.  Dana,  Groth,  Liebisch,  Mallard,  and 
others,  will  make  the  notations  intelligible  to  him. 


THE   TRICLINIC   SYSTEM. 


35 


TABLE  I 

TRICLINIC  FORMS  AND  NOTATIONS 


Form. 

Weiss. 

Naumann. 

Dana. 

Miller. 

Basal-Pinacoids. 

ooa 

006  :  c 

OP 

O  or  c 

001 

Brachy-Pinacoids. 

ooa 

6  :  ooc 

ooPoo 

i-l  or  6 

010 

Macro-Pi  nacoids. 

* 

006  :  ooc 

ooPoo 

i-5  or  a 

100 

a 

b  :  ooc 

00  P' 

J7  orm 

110 

a 

—  6  :  ooc 

00  'P 

'/or  Jf 

no 

Hemi-Prisms. 

a 
a 

nb  :  ooc 
—  nb  :  oo  c 

ooP'n 
oo  'Pn 

i-n' 

MO 

na 

6  :  ooc 

ooP'n 

i-n 

MO 

na 

b  :  ooc 

oo  'Pn 

i-n 

MO 

Hemi-Brachy- 

ooa 

6  :  me 

m/P'oo 

m-! 

05W 

Domes. 

ooa 

—  6  :  me 

m'P/oo 

m-l 

0& 

Hemi-Macro- 

a 

006  :  me 

m'P'oo 

'm-t7 

mi 

Domes. 

—a 

006  :  me 

m^/oo 

/m-*/ 

m 

a 

b:e 

P' 

1 

in 

a 

b':c 

'P 

1 

in 

a 

6:c' 

P* 

1 

nf 

a 

&':c' 

/P 

1 

in 

a 

b  :  me 

mP' 

m' 

hhl 

—a 

b:  me 

m/P 

,m 

hhl 

—  a 

—  b  :  me 

mP/ 

mx 

Jhl 

Tetarto-Pyramids. 

a 

—  b  :  me 

m'P 

'm 

hhl 

a 

nb  :  me 

mP'n 

m-nf 

hkl 

—a 

nb  :  me 

m/Pn 

/m-n 

hkl 

-a 

nb  :  me 

mP/n 

m-nx 

~hkl 

a 

—  nb  :  me 

m/Pn 

'm-n 

hkl 

na 

b  :  me 

mP'n 

m-n' 

hkl 

—  na 

b  :  me 

m/Pn 

/m-n 

hkl 

—  na 

b  :  me 

mP,n 

m-n/ 

hkl 

na 

—  b  :  me 

m'Pn 

'm-n 

hkl 

36  NOTES    ON    CRYSTALLOGRAPHY. 

HEMIHEDRAL    AND    TETARTOHEDRAL    NOTATIONS 

The  previous  account  of  the  notations  particularly 
applies  to  the  holohedral  forms.  The  majority  of 
crystallographers,  however,  indicate  the  hemihedral 
forms  by  writing  J  in  connection  with  the  symbols, 

w'P'oo 
thus  :  \  (a  :  oo  b :  me),  or  -—^ ,  etc.     For  the  tetar- 

tohedral   forms   the   J   is   written  in  the  same  way : 

mP 

J  (a :  b:  me),  or  -7 —  Sometimes  the  forms  are  con- 
sidered "  positive  and  negative,  or  right-handed  and 
left-handed.  These  conditions  are  indicated  by  writ- 
ing -f  or  — ,  or  ±  before  the  symbols,  or  by  writing 
r  or  I  for  right  or  left  before  or  after  the  symbols. 

More  use  is  made  of  this  method  of  writing  the 
symbols  of  the  hemi-  and  tetarto-hedral  forms  in  the 
Isometric  and  Hexagonal  Systems  than  in  any  of  the 
others.  Very  few  writers,  however,  employ  any 
method  of  notation  to  distinguish  the  half  or  quarter 
forms  in  the  Triclinic  System.  In  that  system  all  the 
prisms  and  domes  are  hemihedral  and  all  the  pyra- 
mids are  tetartohedral  forms ;  hence  it  follows  that 
any  plane,  whose  symbol  indicates  that  it  is  a  dome  or 
prism  in  this  system,  must  belong  to  the  half  forms. 
In  like  manner,  if  the  symbol  of  any  face  denotes  that 
it  is  pyramidal,  it  must  belong  to  the  quarter  forms. 
Therefore,  it  is  considered  that  any  special  distinctive 
half  or  quarter  form  marks  are  unnecessary. 


THE   TRICLINIC   SYSTEM.  37 

A  few  writers  distinguish  the  partial  forms  in  the 
Monoclinic  System,  but  the  majority  do  not  use  any  of 
the  characteristic  fractions.  These  fractions  are  used 
chiefly  in  the  other  four  systems,  of  which  the  Hexa- 
gonal and  Isometric  Systems,  as  before  indicated, 
afford  the  majority  of  examples. 

In  the  Miller  System  of  notation  the  symbols,  like 
h  k  I,  stand  for  individual  faces.  Sometimes  these  are 
placed  in  (  ),  as  (h  k  I),  When  they  are  united  to 
make  a.  form,  the  symbols  of  the  plane  have  a  brace  { \ 
written  before  and  after  them,  as  {h  k  l\. 

The  hemihedral  and  tetartohedral  forms  are  indi- 
cated by  writing  some  letter  of  the  Greek  alphabet 
before  the  symbol  of  the  face  or  form  ;  e.  g..  K  for  hemi- 
hedral inclined  faces  and  *  for  hemihedral  parallel 
faces ;  «  { 1  1  1 }  and  *  { h  k  o }. 

The  more  recent  crystallographers  have  largely  dis- 
carded the  use  of  the  terms  holohedral,  hemihedral,  and 
tetartohedral,  and  prefer  to  consider  that  the  six  crys- 
tallographic  systems  are  divided  into  thirty-two  groups 
distinguished  by  their  differences  in  symmetry.  It  is 
here  preferred  to  retain  the  use  of  the  above  terms, 
because  it  is  thought  that,  for  the  present  at  least,  they 
offer  the  fewest  difficulties  to  the  student  who  studies 
crystallography  simply  as  an  aid  in  the  practical  field 
determination  of  minerals. 

Since  the  parameters  of  a  plane  belonging  to  a  half 


38  NOTES   ON   CRYSTALLOGRAPHY. 

or  quarter  form  are  exactly  the  same  as  they  are  when 
this  plane  is  a  constituent  part  of  a  holohedral  form, 
there  is  in  our  common  determinative  work  no  inher- 
ent need  of  distinguishing  the  planes  of  the  different 
partial  forms  from  the  entire  forms. 

They  have  to  be  distinguished  when  drawings  are 
to  be  made,  or  when  an  exact  idea  of  the  form  of  the 
crystal  is  to  be  conveyed.  For  much  of  the  determin- 
ative work  the  special  separation  into  holohedral,  or 
hemihedral,  or  tetartohedral  forms  is  not  required. 
Circumstances  and  particular  conditions  will  deter- 
mine when  the  special  separation  is  desirable. 

DIRECTIONS    FOR    STUDYING    TRICLINIC    CRYSTALS 

1.  Prove  that  the  crystal  or  model  is  triclinic. 

2.  Locate  the  axes  as  previously  directed. 

3.  Note  the  dominant  and  modifying  forms. 

4.  In  giving  the  forms  say  that  the  dominant  form 

is  (naming   the   form);    modified   by  

(naming  the  next  important  subordinate  form);  and  so 
on,  until  all  the  forms  have  been  given. 

5.  Select  and  name  the  pinacoids  by  the  rule. 

6.  Select  and  name  the  dome  and  prism  planes  by 
the  rule. 

7.  Select  and  name  the  pyramidal    or   octahedral 
planes  by  the  rule.    In  naming  the  above  planes,  give, 
first,  all  those  on  the  dominant  form,  and,  secondly,  all 


THE    TRICLINIC    SYSTEM.  39 

the  faces  on  each  secondary  form  in  order  of  the  pre- 
cedence of  those  forms. 

8.  In  naming  the  forms  state  whether  they  are  holo- 
hedral,  hemihedral,  or  tetartohedral.     To  do  this  re- 
member that  if  all  the  similar  planes  of  any  form  are 
present,  that  form  is  holohedral ;  if  one-half  of  all  the 
similar   planes  are  present,  the  form  is  hemihedral; 
and  if  only  one-fourth  of  all  the  similar  planes  are 
present  the  form  is  tetartohedral. 

9.  Locate  the  planes,  axes,  and  centres  of  symmetry, 
if  there  are  any. 

10.  It  is  to  be  noted  that  a  crystal  form  may  have 
as  many  domes  or  prisms  and  octahedrons  as  there  are 
different  positions  in  which  planes  making  these  forms 
can  intersect  the  axes  without  becoming  parallel  to 
any  other  plane ;  but  in   practice   it   is   found   that 
usually  there  are  but  few  forms  of  any  special  class 
(pyramid,  or  dome,  or  prism)  united  in  the  same  com- 
pound form. 


CHAPTER  III 

THE    MONOCLINIC    SYSTEM 

THIS  system  derives  its  name  from  the  Greek  word 
Monos,  "one"  and  Klino,  "  to  incline  or  lean  against," 
from  the  inclination  of  one  axis  to  the  other  two.  In 
this  system  the  axes  are  three  in  number  and  are  un- 
equal in  length  ;  because  it  is  found  that  the  simplest 
variation  from  the  Triclinic  System  is  to  require  that 
two  of  the  axes  be  at  right  angles  to  each  other,  but 
form  oblique  angles  with  the  other  one. 

SYMMETRY 

Before  we  enter  upon  a  fuller  discussion  of  these 
forms,  it  is  best  to  look  at  the  plane  of  symmetry  in 
the  Monoclinic  System.  In  this  system  an  examina- 
tion of  the  crystals  shows  that  there  is  one  direction, 
and  only  one,  in  which,  if  a  plane  be  passed  through 
the  crystal,  it  \fill  make  a  division  into  two  equal  and 
symmetrical  halves.  This  single  plane  of  symmetry 
occurs  only  in  the  Monoclinic  System,  with  but  three 
exceptions  in  other  systems.  See  Figs.  198  and  199. 

The  exceptions  can  be  distinguished  by  the  fact  that 
(40) 


THE    MONOCLINIC    SYSTEM.  41 

the  Monoclinic  System  has  in  the  normal  forms  an 
axis  of  binary  symmetry  only,  while  the  three  excep- 
tions have,  respectively,  axes  of  trigonal,  tetragonal, 
and  hexagonal  symmetry.  It  should  be  particularly 
noted  that  the  axis  of  binary  symmetry  in  the  Mono- 
clinic  System  is  perpendicular  to  the  plane  of  sym- 
metry. In  this  system  the  normal  forms  have  a  centre 
of  symmetry.  See  Figs.  8-11  and  59-86. 

NOMENCLATURE 

In  the  Monoclinic  System  it  is  customary  to  locate 
the  plane  of  symmetry  first  and  the  axis  of  symmetry 
next. 

As  a  rule,  a  Monoclinic  crystal  placed  on  end  will 
rest  on  one  of  two  parallel  planes  or  edges,  and  the 
shortest  line  joining  them  will  be  the  vertical  axis. 
See  Figs.  9-11,  60,  64,  71,  78,  and  83. 

Having  ascertained  the  plane  and  the  axis  of  sym- 
metry, place  the  crystal  on  its  base  or  basal  edge,  and 
consider  an  axis  to  lie  in  that  plane  of  symmetry,  and 
to  be  drawn  from  the  base  parallel  to  the  side  planes 
and  edges.  As  before  stated,  this  axis  is  called  the 
Vertical  Axis.  See  c,  Figs.  2,  60,  and  64.  Of  the 
other  two  axes  one  must  be  coincident  with  the  axis 
of  binary  symmetry  and  therefore  perpendicular  to 
the  plane  of  symmetry.  The  other  axis  must  lie  in 
the  plane  of  symmetry  and  must  be  drawn,  as  a  rule, 


42  NOTES    ON    CRYSTALLOGRAPHY. 

parallel "  to  the  base  or  basal  edge.  Both  these  axes 
are  called  Lateral  Axes.  The  one  that  is  perpendicu- 
lar to  the  plane  of  symmetry  is  named  the  Ortho-Axis 
(see  ~b,  Figs.  2,  60,  and  64)  or  the  Ortho -Diagonal 
(Greek,  Orthos,  "  in  a  straight  or  right  line  ") ;  while 
the  other  lateral  axis,  or  the  one  lying  in  the  plane  of 
symmetry,  is  called  the  Clino-Axis  (see  d,  Figs.  2,  60, 
and  64),  or  Clino -Diagonal  (Greek,  Klino,  "  to  incline, 
or  to  make  a  slope  or  slant,  or  to  lean  against"). 
From  these  meanings  the  Ortho-Axis  is  often  called 
the  Straight  Axis  and  the  Clino-Axis  the  Inclined  or 
Oblique  Axis. 

In  this  case,  as  in  the  preceding  one,  planes  may  in- 
tersect only  one  axis,  or  cut  two  axes,  or  intersect  all 
three,  giving  us  as  before  Pinacoids,  Domes  or  Prisms, 
and  Pyramids  or  Octahedrons. 

In  the  naming  of  pinacoids  in  the  Monoclinic  Sys- 
tem, their  relations  to  the  axes  are  used,  as  in  the  Tri- 
clinic  System.  As  the  Monoclinic  lateral  axes  have 
different  names  from  the  Triclinic  lateral  axes,  the 
nomenclature  will,  in  that  respect,  vary  in  the  two 
systems.  From  this  it  follows : 

1.  If  a  pinacoid  cuts  the  vertical  axis  and  is  par- 
allel to  the  two  lateral  axes,  it  is  a  Vertical  Pinacoid ; 
but  it  is  generally  called  a  Basal  Plane,  or  a  Basal 
Pinacoid.  See  001,  Figs.  59-63,  65-70,  and  73-77. 
On  the  other  hand,  the  lateral  pinacoids  are  named 


THE    MQNOCLINIC    SYSTEM.  43 

from  the  lateral  axis  to  which  they  are  parallel ;  as, 
for  example,  if  a  pinacoid  intersects  the  ortho-axis  and 
is  parallel  to  the  clino-axis,  it  is  a  Clino -Pinacoid 
(see  010,  Figs.  61,  67-72,  74,  75,  77,  and  81-86);  if 
it  cuts  the  clino-axis  and  is  parallel  to  the  ortho-axis, 
it  is  designated  as  an  Ortho-Pinacoid  (see  100,  Figs. 
59,  61,  62,  65,  68,  71,  72,  78,  and  83). 

2.  The  dome  or  prism  planes  are  named  from  the 
axis  to  which  they  are  parallel.     Thus  they  are  called 
Clino-Dome  Planes  if  they  are  parallel  to  the  clino- 
axis  (see  Oil,  Figs.  65,  70,  75,  and  84) ;  but  they  are 
named  Ortho-Dome  Planes  if  they  are  parallel  to  the 
ortho-axis  (see  401,  102,  Fig.  69 ;  and  101,  Figs.  65, 
66,  70,  and  79) ;  and  they  are  called  Vertical  Dome 
Planes,  or  more  commonly  Prism  Planes,  if  they  are 
parallel  to  the  vertical  axis  (see  110,  Figs.  59,  60,  62, 
63,  65-72,  74-77,  and  82-86). 

3.  If  a  plane  cuts  all  three  axis,  it  is  a  Pyramidal 
or  Octahedral  Plane.     See  111,  Figs.  64,  68,  69,  71, 
72,  77-83,  85,  and  86. 

RELATION  OF  PLANES  TO  THE  AXES 

To  enable  one  to  name  the  crystal  planes  in  the 
easiest  way,  it  is  best,  as  a  rule,  to  locate  the  axes 
parallel  to  the  largest  number  of  planes  possible ;  i.  e., 
to  make  as  many  pinacoids,  domes,  and  prisms  as  pos- 
sible, and  as  few  pyramids  or  octahedrons  as  possible. 


44  NOTES    ON    CRYSTALLOGRAPHY. 

DISTINGUISHING  CHARACTERISTICS   OF   THE   MONOCLINIC 
CRYSTALS 

See  whether  or  not  the  form  belongs  in  the  Mono- 
clinic  System,  determining  this,  first,  by  the  presence 
of  one  plane  of  symmetry  and  one  binary  axis  of  sym- 
metry only,  and  next,  by  the  fact  that  the  edges  and 
planes  at  the  ends  of  the  crystals  make  oblique  angles 
with  the  edges  and  planes  on  the  sides,  so  that  when  a 
model  or  perfect  crystal  is  set  on  end,  with  an  end 
plane  or  edge  parallel  to  the  table,  it  leans  backwards, 
forming  oblique  angles  with  the  table,  but  without 
any  sidewise  twist,  as  is  the  case  with  the  Triclinic 
Crystals.  See  Figs.  28-35  for  Triclinic  Crystals,  and 
Figs.  8-11,  and  59-86  for  Monoclinic  Crystals. 

RULES  FOR  NAMING  MONOCLINIC  PLANES 

I.  If  a  plane  cuts  one  axis  and  is  parallel  to  the 
other  two,  it  is  a  Pinacoid.     If  it  cuts  the  vertical  axis, 
it  is  a  Basal  or  Vertical  Pinacoid,  or  a  Basal  Plane ;  if 
it  intersects  the  ortho-axis,  it  is  a  Clino-Pinacoid ;  if  it 
cuts  the  clino-axis,  it  is  an  Ortho-Pinacoid. 

II.  If  a  plane  cuts  two  axes  and  is  parallel  to  the 
third  axis,  it  is  a  Dome  or  Prism  Plane,  and  is  named 
from  the  axis  to  which  it  is  parallel ;  if  it  is  parallel  to 
the  vertical  axis,  it  is  a  Prism  or  Vertical  Dome  Plane  ; 
if  parallel  to  the  clino-axis,  it  is  a  Clino-Dome  Plane ; 
if  parallel  to  the  ortho-axis,  it  is  an  Ortho-Pome  Plane, 


THE    MONOCLINIC    SYSTEM.  45 

III.  If  a  plane  cuts  three  axes,  it  is  a  Pyramidal 
or  Octahedral  plane. 

HOLOHEDRAL    FORMS 

The  Holohedral  Forms  in  this  system  are  the  prisms 
(vertical  domes)  and  the  clino-domes. 

HEMIHEDRAL    FORMS 

The  Hemihedral  Forms  in  this  system  are  the  ortho- 
domes  and  pyramids  or  octahedrons;  hence,  all  are 
properly  called  Hemi-Ortho-Domes  and  Hemi-Pyra- 
mids  or  Hemi- Octahedrons.  They  can  be  distinguished 
by  their  conformity  to  the  laws  for  dome  and  pyramidal 
planes,  and  by  the  fact  that  they  modify  only  one-half 
the  similar  planes  upon  the  crystal.  See  Figs.  62,  63, 
65  72,  75-77,  and  79-86. 

HEMIMORPHISM 

The  term  Hemimorphism  is  employed  to  describe 
crystals  whose  opposite  ends  are  unlike,  i.  e.,  composed 
of  different  half-forms  or  of  unlike  planes  (Greek, 
Morphe,  "form"  or  "  shape").  A  requirement  of  true 
Hemimorphism  is  that  these  dissimilar  planes  or  half- 
forms  shall  be  at  opposite  ends  of  an  axis  of  symmetry, 
which  must  also  be  a  crystallographic  axis.  See  Figs. 
87  and  88. 

No  true  hemimorphic  forms  occur  amongst  the 
minerals  crystallizing  in  the  Monoclinic  System  ;  but 


46  NOTES    ON   CRYSTALLOGRAPHY. 

there  is  one  pseudo-hemimorphic  form  that  needs  to 
be  considered  here.  It  is  the  rare  mineral  clinohe- 
drite  (''inclined  planes"),  which  is  placed  by  itself  in 
the  Clinohedral  Group.  '  While  this  form  resembles  a 
hemimorphic  form,  it  fails  to  be  so  classed  because  it 
lacks  the  essential  characteristic  of  the  hemimorphic 
forms,  an  axis  of  symmetry.  This  pseudo-hemimor- 
phic form  has  neither  axis  nor  centre  of  symmetry, 
but  it  does  have  a  plane  of  symmetry. 

COMPOUND    FORMS 

The  compound  forms  of  this  system  are  compara- 
tively simple,  consisting  of  prisms,  domes,  and  pina- 
coids ;  sometimes  with  hemi-pyramids,  but  more  usu- 
ally without  them  in  the  commoner  forms.  It  is  to 
be  remembered  that  the  holohedral  and  hemihedral 
forms  are  to  be  distinguished  by  the  presence  of  all 
the  possible  similar  planes  for  the  holohedral  forms, 
and  by  the  presence  of  half  the  number  of  possible 
similar  planes  for  the  hemihedral  forms.  See  Figs. 
8-11,  59-86. 

READING   DRAWINGS   OF   MONOCLINIC    CRYSTALS 

In  this  system  the  letters  used  to  designate  the  axes 
are  the  same  as  those  employed  in  the  Triclinic  Sys- 
tem ;  but  for  one  of  the  lateral  axes,  the  clino-axis,  the 
distinguishing  mark  is  the  grave  accent  over  the  semi- 
axis  letter,  thus  d.  Some  authors,  notably  the  Danas, 


THE    MONOCLINIC    SYSTEM.  47 

change  the  mark  over  the  ortho-semi-axis  letter  6 ;  e.  g., 
instead  of  writing  6,  they  write  b,  using  the  sign  _L-  to 
indicate  the  straight  or  ortho-axis  or  the  perpendicular 
axis.  Our  axial  letters  and  signs  are  then  as  follows  : 

Clino-Semi-Axis,  d. 

Ortho-Semi-Axis,  b  or  b. 

Vertical  Semi-Axis,  c. 

Practically,  then,  the  notation  in  the  Monoclinic 
System  will  be  similar  to  that  of  the  Tri clinic  System, 
the  variations  being  due  to  the  different  positions  of 
the  axes.  The  positive  and  negative  signs  for  the 
parameters  and  indices  are  used  as  in  the  Triclinic 
System.  See  Figs.  2,  60,  and  64. 

Thus,  in  the  Weiss  notation,  the  symbols  of  the 
Vertical  Pinacoid  or  Basal  Plane  are  oo  d  :  oo  6  :  c. 
This  is  abbreviated  in  the  Naumann  system  as  0  P; 
in  Dana's  as  0;  and  in  Miller's  as  0  0  1.  See  Fig.  61. 

In  the  Naumann  symbols  the  clino-axis  or  ortho- 
axis  is  marked  either  by  this  Px  or  by  P;  some,  how- 
ever, place  the  axial  mark  over  the  letters  or  the 
infinity  symbol  that  accompanies  the  P,  as  oo  Pn  or 
oo  P  n,  while  others  omit  the  marks.  Table  II,  giving 
the  Weiss,  Naumann,  Dana  and  Miller  symbols,  it  is 
hoped,  will  make  the  different  systems  of  symbols  suf- 
ficiently clear  to  the  student,  especially  if  he  will 
study  Figs.  8-11  and  59-86. 


48 


NOTES    ON    CRYSTALLOGRAPHY. 


As  previously  stated,  only  a  very  few  crystallo- 
graphers  distinguish  by  symbols  the  hemihedral  forms 
in  the  Monoclinic  System,  which  has  no  tetartohedral 
forms  amongst  the  minerals. 

TABLE  II 

MONOCLINIC  FORMS  AND  NOTATIONS 


Form. 

Weiss. 

Naumann. 

Dana. 

Miller. 

Basal  Pinacoids. 

cca 

006  :c 

OP 

O  or  c 

001 

Clino-Pinacoids. 

ooa 

6  :  QOC 

QOPOO 

i-i  or  b 

010 

Ortho-Pinacoids. 

a 

oo  6  :  oo  c 

GOPOO 

i-i  or  a 

100 

a 

6  :  ooc 

OOP 

lor  m 

110 

Prisms. 

na 

6  :  coc 

oo  Pn 

i-n 

hkO 

a 

nb  :  oo  c 

voPn 

i-n 

hldb 

Clinodomes. 

cca 

b  :  me 

mPoo 

m-\ 

w 

Hemi- 
Orthodomes. 

a 
a 

006  :  me 
oo  b  :-mc 

-raPoo 
mP(x> 

-m-i 
m-i 

mi 

JiQl 

a 

b:-c 

P 

1 

ni 

a 

b:c 

-P 

-1 

111 

a 

b  :-mc 

mP 

m 

~hhl 

Hemi-Pyramids. 

a 
na 

b  :  me 
b  :-mc 

-mP 
mPn 

-m 
m-n 

hhl 
~hkl 

na 

b  :  me 

-mPn 

-m-n 

hkl 

a 

nb  :-mc 

mPn 

m-n 

~hkl 

a 

nb  :  me 

-mPn 

-m-n 

hkl 

THE    MONOCLINIC    SYSTEM.  49 

DIRECTIONS    FOR    STUDYING    MONOCLINIC    CRYSTALS 

1.  Prove  that  the  crystal  or  model  is  Monoclinic. 

2.  Determine  the  plane  and  the  axis  of  symmetry ; 
remembering  that  a   single   extremely    rare   pseudo- 
hem  imorphic   (clinohedral)   form  alone,  amongst  the 
Monoclinic  minerals,  has  no  axis  of  symmetry. 

3.  Locate  the  axes,  as  previously  directed. 

4.  Note  the  dominant  and  modifying  forms  in  the 
order  of  their  importance. 

5.  Select  and  name  the  planes  of  each  form  in  the 
following  order :  pinacoids,  prisms,  domes,  and  pyra- 
mids. 

6.  Distinguish    the    holohedral,    hemihedral,    and 
pseudo-hemimorphic  or  clinohedral  forms. 

4 


CHAPTER  IV 

THE    ORTHORHOMBIC    SYSTEM 

THIS  system  derives  its  name  from  the  Greek, 
Orthos,  "  straight "  or  "  right/'  and  Ehombos,  "  a 
rhomb,"  because  its  similar  planes  commonly  form 
right  rhombs. 

Continuing  to  vary  the  axes  and  angles,  we  note 
that  this  system  must  have  all  its  axial  angles  right 
angles,  while  the  axes  still  remain  of  unequal  length. 

NOMENCLATURE 

Since  the  axes  are  of  unequal  length,  it  is  necessary 
to  distinguish  each  semi-axis  by  distinctive  names  and 
letters.  This  is  done  by  using  the  same  nomenclature 
as  in  the  Triclinic  System :  Brachy-Semi-Axis,  a ; 
Macro-Semi-Axis,  1 ;  and  Vertical  Semi- Axis,  c,  re- 
spectively. See  Fig.  3. 

As  before,  the  planes  may  intersect  one  axis  and  be 
parallel  to  the  other  two,  forming  Pinacoidal  Planes 
(see  100,  001,  and  010,  Figs.  87-94,  97, 101-104,  108, 
109,  118,  120-122,  125-129,  and  131-135) ;  or  they 
may  cut  two  axes  and  be  parallel  to  the  third  axis, 
making  Dome  and  Prism  Planes  (see  110,  101,  Oil, 

(50) 


THE    ORTHORHOMBIC    SYSTEM.  Si 

120,  210,  012,  and  021,  Figs.  87-104,  113,  115,  117- 

121,  and  123-135) ;  or  they  may  intersect  all  three 
axes,  forming  Pyramidal  or  Octahedral  Planes  (see 
111,  Figs.  87,  88,  91,  92,  96,  97,  105-129  and  131- 
135). 

In  naming  the  above  planes  we  proceed  as  we  did 
in  the  Triclinic  System,  using  the  same  nomenclature. 
The  student  is  referred  to  that  system  for  the  method. 

RELATION   OF   PLANES   TO    AXES 

In  this  system,  as  in  the  preceding  systems,  we 
place  the  axes,  as  a  rule,  so  that  they  are  parallel  to 
the  greatest  number  of  planes  possible ;  i.  e.,  to  make 
as  many  pinacoids  and  as  many  domes  and  prisms  as 
possible,  and  as  few  pyramids  as  possible. 

SYMMETRY 

In  this  system  the  normal  forms  have  three  planes 
of  symmetry  coinciding  in  direction  with  the  three 
axes  of  the  system,  and  therefore  at  right  angles  to  one 
another.  See  Figs.  3,  7,  51,  and  87-135. 

The  normal  orthorhombic  forms  further  have  three 
axes  of  binary  symmetry  which  are  coincident  with 
the  three  unequal  crystal  axes. 

In  the  Isometric  System  the  Pyritohedron  or  Penta- 
gonal Dodecahedron  (see  Figs.  52  and  53),  and  the 
Diploid  or  Dyakis-Dodecahedron  (see  Figs.  136  and 
137),  have  also  three  planes  of  symmetry  only,  which 


52  ttOTES   ON    CRYSTALLOGRAPHY. 

are  at  right  angles  to  one  another.  These  forms  need 
not  be  mistaken  for  Orthorhombic  crystals,  since  they 
are  of  equal  dimensions  along  each  plane  of  symmetry, 
while  in  the  Orthorhombic  forms  the  dimensions  are 
unequal. 

The  above  Isometric  forms  also  have  three  axes  of 
binary  symmetry  that  are  coincident  with  the  equal 
crystal  axes,  and  they  further  have  four  axes  of 
trigonal  symmetry. 

In  the  Hexagonal  System  the  rhombohedral  (see 
(Figs.  138  and  139),  and  scalenohedral  (see  Figs.  140 
and  141)  forms  have  also  three  planes  of  symmetry, 
but  these  form  angles  of  60°  with  one  another,  and  all 
extend  in  the  same  direction  ;  i.  e.,  they  lie  in  the 
plane  of  the  vertical  axis,  instead  of  forming  right 
angles  with  one  another,  as  in  the  Orthorhombic 
System. 

The  Rhombohedron  and  Scalenohedron  also  have 
three  axes  of  binary  symmetry,  but  they  all  lie  in  the 
plane  of  the  lateral  axes.  They  also  have  a  vertical 
axis  of  trigonal  symmetry  coincident  with  the  vertical 
crystal  axis.  Further,  the  three  lateral  dimensions  of 
the  Hexagonal  crystals  are  the  same,  but  all  the 
dimensions  are  unequal  in  the  Orthorhombic  forms ; 
while  the  similar  parts  are  three  or  some  multiple  of 
three  in  the  Hexagonal  System,  and  but  two  or  four 
or  some  multiple  of  four  in  the  Orthorhombic  System. 


THE    ORTHORHOMBIC    SYSTEM.  53 

DISTINGUISHING    CHARACTERISTICS    OF    THE    ORTHO- 
RHOMBIC    CRYSTALS 

1.  Determine  whether  or  not  the  crystal  or  crystal 
model  belongs  to  the  Orthorhombic  System.     This  can 
easily  be  done  by  noting  the  three  unequal  dimensions 
of  the  crystal ;  by   observing  that  these  dimensions 
form  right  angles  with  one  another ;  by  noticing  the 
presence  in  the  normal  forms  of  but  three  planes  of 
symmetry  arranged  at  right  angles  with  one  another 
and  parallel  to  the  three  unequal  directions  shown  on 
the  crystal ;  by  noting  that  the  three  axes  Of  binary 
symmetry  lie  in  the  three  planes  of  symmetry  and 
coincide  with  the  three  crystal  axes ;  and  by  observing 
that  the  similar  parts  at  the  ends,  or  on  the  sides  of 
the  crystal,  are  in  twos  or  fours,  but  never  in  threes  or 
any  multiple  of  three. 

2.  Having   determined   that   the  crystal   is   ortho- 
rhombic,  place  it  generally  with  its  thinnest  direction 
in  a  vertical  position.     In  many  cases  this  gives  a 
basal  plane  or  pinacoid  for  it  to  rest  upon.     Call  the 
direction  perpendicular  to  the  table  the  vertical  axis ; 
then  imagine  the  planes  of  the  ends  prolonged  until 
they  meet  or  intersect.     Consider  then  the  longer  of 
the  two  lateral  directions  thus  formed  the  macro-axis, 
and   the  shorter  will   be  the   brachy-axis.     It  often 
happens  that  if  we  imagine  the  crystal  planes  to  be 
prolonged  until  they  meet  one  another,  the  apparently 


54  NOTES   ON    CRYSTALLOGRAPHY. 

shortest  length  of  the  crystal  is  the  longest  dimension. 
If  the  axes  are  properly  selected  in  the  normal  forms, 
they  will  lie  in  the  three  planes  of  symmetry  and  will 
coincide  with  the  three  axes  of  binary  symmetry. 

RULES    FOR    NAMING    ORTHORHOMBIC    PLANES 

I.  A  plane  which  intersects  one  axis  and  is  parallel 
to  the  other  two  is  a  Pinacoidal  Plane.     If  it  cuts  the 
vertical  axis,   it  is    called    a  Basal  Pinacoid  or  Basal 
Plane.     If  it  intersects  the  brachy-axis,  it  is  an  Ortho- 
Pinacoid.     If  it  cuts  the  ortho-axis,  it  is  a  Brachy- 
Pinacoid. 

II.  If  the  plane  intersects  two  axes  and  is  parallel 
to  the  third  axis,  it  is  a  Dome  or  Prism  Plane.    If  this 
plane  is  parallel  to  the  vertical  axis,  it  is  known  as  a 
Vertical  Dome  Plane,  or  more  usually  as  a  Prism 
Plane;   if  parallel   to   the   clino-axis,   it   is   a   Clino- 
Dome  Plane ;  if  parallel  to  the  ortho-axis,  it  is  an 
Ortho-Dome  Plane. 

III.  If  the  plane  intersects  all  three  axes,  it  is  a 
Pyramidal  or  Octahedral  Plane. 

IV.  In  case  the  form  has  only  half  the  full  num- 
ber of  faces,  give  to  that  form  the  name  of  the  hemi- 
hedral  form  that  has  the  same  parameters. 

HOLOHEDRAL   FORMS 

Most  of  the  common  crystals  of  the  Orthorhombic 
System   are   composed   of  holohedral   forms.     These 


THE   ORTHORHOMBIC   SYSTEM.  55 

forms  have,  as  previously  stated,  three  planes  of  sym- 
metry and  three  axes  of  binary  symmetry. 

HEMIHEDRAL    FORMS 

The  hemi-domes  and  hemi-prisms  are  not  very  com- 
mon in  this  system,  and  when  they  do  occur  they  can 
be  recognized  by  their  modification  of  only  one-half 
the  similar  parts  of  the  dominant  form. 

The  more  commonly-occurring  forms  are  hemi- 
pyramids,  which  produce  wedge-shaped  forms  called 
Sphenoids  (Greek,  Sphen,  "  a  wedge  ").  For  purposes 
of  distinction  these  forms  are  often  called  Orthorhom- 
bic  Sphenoids.  They  are  characterized  by  their 
wedge-  or  axe-shaped  edges;  arid  are  distinguished 
from  the  wedge-shaped  forms  in  the  other  systems  by 
their  three  unequal  dimensions,  by  the  fact  that  their 
faces  are  scalene  triangles,  by  the  possession  of  three 
axes  of  binary  symmetry,  and  by  their  lack  of  any 
plane  or  centre  of  symmetry.  See  Figs.  88  and  142- 
150.  Figs.  88,  149,  and  150  show  how  a  sphenoid 
modifies  the  opposite  ends  of  a  crystal,  producing  a 
form  that  might  be  mistaken  for  a  hemimorphic  one. 

The  formation  of  the  Sphenoids  can  be  easily  under- 
stood if  we  will  take  a  simple  pyramid  and  consider 
one-half  of  its  planes  obliterated  (i.  e.,  alternate  planes), 
and  enlarge  the  other  four  alternate  planes  until  they 
meet  and  make  a  complete  form.  Fig.  235  shows  by 


56  NOTES    ON    CRYSTALLOGRAPHY. 

its  blackened  planes  the  faces  to  be  obliterated.  See 
Figs.  145  and  146.  We  can  illustrate  this  for  our- 
selves by  pasting  sheets  of  paper  to  the  alternate  faces 
of  a  model  of  a  pyramid,  and  trimming  the  sheets 
until  they  join  at  their  edges,  making  a  completed  form. 

It  is  illustrated  better  by  the  glass  models  made  in 
Germany,  which  show  paper  pyramids  on  the  inside 
of  the  models  with  the  alternate  faces  carried  out  in 
glass,  until  they  meet,  making  glass  sphenoids. 

The  above  method  of  derivation  of  the  sphenoid 
shows  that  another  sphenoid  can  be  formed  if  we  carry 
out  the  planes  which  we  before  considered  suppressed 
and  then  look  upon  the  others  as  obliterated.  We 
may  designate  these  two  sphenoids  as  positive  and  nega- 
tive ;  or  as  they  are  related  to  each  other  as  the  right 
hand  is  to  the  left  hand,  it  is  usual  to  call  the  positive 
sphenoids  right-handed  and  the  negative  ones  left- 
handed. 

HEMIMORPHIC  FORMS 

Fig.  87  represents  a  hemirnorphic  form  of  this  sys- 
tem and  shows  distinctly  the  different  planes  modify- 
ing the  opposite  ends  of  the  crystal. 

In  this  system  the  hemimorphic  forms  have  two  dis- 
similar planes  of  symmetry  and  one  axis  of  binary 
symmetry,  but  they  are  destitute  of  a  centre  of  sym- 
metry. 


THE   ORTHORHOMBIC    SYSTEM.  57 

COMPOUND  FORMS 

The  more  usual  compound  forms  in  the  Orthorhom- 
bic  System  are  composed  of  pinacoids,  prisms,  and 
domes,  sometimes  without  pyramids,  but  oftener  with 
them,  The  holohedral  forms  are  the  most  common, 
but  these  forms  are  not  infrequently  associated  with 
hemihedral  or  hemimorphic  forms.  The  heinihedral 
forms  can  be  distinguished  readily  by  the  fact  that 
they  have  half  the  number  of  possible  similar  planes. 
The  hemimorphic  forms  can  be  determined  by  the  fact 
that  the  planes  at  the  opposite  ends  of  a  crystal  axis 
(which  is  also  an  axis  of  symmetry)  are  dissimilar. 
See  Figs.  87  135. 

READING  DRAWINGS  OF  ORTHORHOMBIC  CRYSTALS 

As  previously  mentioned  the  notation  for  the  axes 
of  the  Orthorhombic  System  is  as  follows  : 

Brachy-Semi-Axis,  a. 

Macro-Semi-Axis,  b. 

Vertical  Semi-Axis,  c. 

See  Fig.  3. 

These  symbols  are  considered  positive  or  negative 
under  the  same  rules  as  those  given  under  the  Tri- 
clinic  System. 

The  notations  in  this  system  will  then  be  almost 
identical  with  those  of  the  Triclinic  System.  This 
fact  leads  to  the  belief  that  the  Orthorhombic  notations 
will  not  offer  any  difficulties  to  the  student  who  has 
mastered  the  Triclinic  notations. 


58 


NOTES    ON    CRYSTALLOGRAPHY. 


The  methods  employed  for  distinguishing  the  right 
or  positive  sphenoids  from  the  left  or  negative  ones  are 
shown  sufficiently  well  in  Table  III,  so  that  the  stu- 
dent should  have  no  difficulty  in  understanding  the 
notations, 

TABLE  III 

ORTHORHOMBIC  FORMS  AND  NOTATIONS 


Forms. 

Weiss. 

Naumann. 

Dana. 

Miller. 

Basal 

Pinacoids. 

GO  a    GO  b  i     c 

OP 

Oorc 

001 

Brachy- 

Pinacoids. 

ooa        b  '.  coc 

coPcc 

i-i  or  & 

010 

Macro- 

Pinacoids. 

a    006  :  coc 

coPco 

i-i  or  a 

100 

a       b  :  ooc 

ccP 

Jor  w 

110 

Prisms. 

na       6:  coc 

coPn 

i-n 

hkO 

a     nb  :  coc 

coPn 

i-n 

hkO 

Brachy- 

Domes. 

oo  a       6  :  me 

wPco 

m-l 

Okl 

Macro- 

Domes. 

a    co  6  :  we 

wPco 

m-i 

hQl 

a       6  :     c 

p 

1 

111 

Pyramids. 

a       6  :  me 
na       b:  me 

wP 
mPn 

w 
w-n 

hhl 
hkl 

a     nb  :  me 

mPn 

m-n 

hkl 

+orri(  d  :  b  :  me) 

+  orr^ 

-f-  or  r  — 

K\hhl\ 

—  or  Z£  (  a  :  b  :  me) 

~2" 

—  or  Z  m 

K\hhl\ 

Sphenoids. 

+orr  lf(na  :  b  :mc) 

J-  nr  v  WiP11 

_j_  nj.^.^-^ 

K\hkl\ 

2 

2 

—or  1$  (na  :  b  :  me) 

7  wPn 

or  j|  m-n 

K\hkll 

2 

2 

+  orrl(a-nb'  we) 

+      r  wPn 

4.      r  m-n 

+ 

_      - 

-      Z       2 

I     2 

K\hkl\ 

THE    ORTHORHOMBIC    SYSTEM.  59 

DIRECTIONS     FOR     STUDYING     ORTHORHOMBIC    CRYSTALS 

1.  Prove  that  the  crystal  or  model  is  orthorhombic. 

2.  Locate  the  axes,  as  previously  directed. 

3.  Note  the  dominant  and  modifying  forms  in  the 
order  of  their  importance. 

4.  Select  and  name  the  planes  of  each  form  in  the 
following  order :  pinacoids,  prisms,  domes,  and  pyra- 
mids. 

5.  Distinguish    the    holohedral,    heniihedral,    and 
hemimorphic  forms,  designating  the  sphenoids  as  such. 

6.  Locate  the  planes,  axes,  and  centres  of  symmetry. 


CHAPTER  V 

THE    TETRAGONAL    SYSTEM 

In  the  next  variation  that  leads  to  the  formation  of 
another  system  all  the  angles  are  right  angles,  but  two 
of  the  axes  are  equal,  and  the  third  one  is  unequal  in 
length  to  the  other  two. 

The  only  requirement  is  that  this  third  axis  must 
be  either  longer  or  shorter  than  the  other  two  and  must 
be  perpendicular  to  them.  This  variable  axis  is  always 
selected  as  the  Vertical  Axis.  The  other  two  axes,  also 
lying  so  as  to  make  right  angles  with  each  other,  as 
well  as  with  the  Vertical  Axis,  are  called  Lateral  Axes. 
See  Figs.  4  and  162. 

NOMENCLATURE 

In  this  system  the  nomenclature  differs  somewhat 
from  that  followed  in  the  three  preceding  systems,  be- 
coming more  complicated. 

I.  If  a  plane  cuts  the  vertical  axis  and  is  parallel  to 
the  lateral  axes,  it  is  called  a  Basal  Pinacoid  or  Basal 
Plane.  See  Figs.  147-149.  There  can  be  but  two  such 
planes  on  any  crystal. 

(60) 


THE    TETRAGONAL    SYSTEM.  61 

II.  Of  lateral  planes  parallel  to  the  vertical  axis 
three  cases  may  occur : 

1.  The  plane  may  cut  both  lateral  axes  equally,  giv- 
ing rise  to  a  Primary  or  Direct  Prism  Plane,  frequently 
called  a  Prismatic  Plane  of  the  First  Order.     See  110, 
Figs.  147,  150,  and  157. 

2.  If  the   before-mentioned    plane   cuts   only    one 
lateral  axis  and  is  parallel  to  the  other,  it  is  known  as 
a  Secondary  or  Inverse  Prism  Plane,  or  as  a  Prismatic 
Plane  of  the  Second  Order.     See  100  and  010,  Figs. 
152,  153,  and  156-159,  174,  183,  188,  and  190. 

3.  If  the  aforesaid  plane  cuts  the  two  lateral  axes  at 
unequal  distances,  it  is  called  a  Ditetragonal  Prism 
Plane.     See  h  k  0,  Figs.  160,  161,  and  189  ;  and  320, 
Fig.  190. 

III.  Again,  if  a  plane  cuts  the  vertical  axis  and  in- 
tersects one  or  both  lateral  axes,  it  is  called  a  Pyramidal 
or  Octahedral  Plane.     Of  Pyramidal  Planes  there  may 
also  be  three  cases  : 

1.  If  the  plane  in  question  cuts  both  lateral  axes 
equally,  it  is  known  as  a  Primary  or  Direct  Pyramidal 
or  Octahedral  Plane,  or  as  a  Pyramidal  Plane  of  the 
First  Order.     See  111,  Figs.  154,  155,  157,  159,  162, 
164,  166-183,  and  185-191. 

2.  If  it  cuts  only  one  lateral  axis  and  is  parallel  to 
the  other,  it  is  known  as  a  Secondary  or  Inverse  Pyra- 
midal Plane,  or  as  a  Pyramidal  Plane  of  the  Second 


62  NOTES   ON   CRYSTALLOGRAPHY. 

Order.     See  101,  Oil,  and  h  0  Z,  Figs.  156,  163,  165, 
and  175-182. 

3.  If  it  cuts  both  lateral  axes  at  unequal  distances, 
it  is  called  a  Ditetragonal  Pyramidal  Plane,  or  a  Zir- 
conoidal  Plane,  or  a  Dioctahedral  Plane.  See  h  k  I, 
Figs.  160  and  184-186;  313,  Figs.  187  and  188;  and 
321,  Fig.  191. 

RELATIONS  OF  THE  PLANES  TO  THE  AXES 

As  in  the  preceding  system,  the  axes  are  to  be 
located  so  as  to  have  upon  the  crystal  as  many  pina- 
coids  and  prisms  as  possible,  with  the  fewest  possible 
pyramids. 

DISTINGUISHING  CHARACTERISTICS  OF  TETRAGONAL 
CRYSTALS 

Crystals  that  belong  in  this  system  are  generally 
distinguished  by  the  possession  of  two  equal  exten- 
sions and  one  unequal ;  by  the  fact  that  the  opposite 
ends  of  the  unequal  extension  are  similar  ;  and  by  the 
further  fact  that  the  planes  at  the  ends  of  the  unequal 
extension  are  commonly  in  twos,  fours,  or  eights ;  or 
that  the  vertical  axis  (the  axis  of  unequal  extension) 
is  coincident  with  an  axis  of  binary  or  tetragonal 
symmetry. 

RULES  FOR  NAMING  TETRAGONAL  PLANES 

I.  Any  plane  parallel  to  both  the  lateral  axes  is  a 


THE    TETRAGONAL   SYSTEM.  63 

Pinacoid,  and  is  called  a  Basal  Pinacoid  or  a  Basal 
Plane. 

II.  Any  plane  which  cuts  one  or  more  lateral  axes 
and  is  parallel  to  the  vertical  axis  is  a  Prismatic  Plane. 
If  it  intersects  both  lateral  axes  equally,  it  is  a  Primary 
or  Direct  Prismatic  Plane,  or  a  Prismatic  Plane  of  the 
First  Order ;  if  it  intersects  one  lateral  axis  but  is 
parallel  to  the  other,  it  is  a  Secondary  or  Inverse 
Prismatic  Plane,  or  a  Prismatic  Plane  of  the  Second 
Order ;  but  if  it  cuts  the  lateral  axes  unequally,  it  is 
a  Ditetragonal  or  Dioctahedral  Prismatic  Plane. 

III.  If  the  plane  cuts  all  three  axes,  it  is  a  Pyra- 
midal or  Octahedral  Plane.     If  it  cuts  the  two  lateral 
axes  equally,  it  is  a  Primary  or  Direct  Pyramidal  or 
Direct  Octahedral  Plane,  or  a  Pyramidal  Plane  of  the 
First  Order.     If  it  intersects  one  lateral  axis  and  is 
parallel  to  the  other,  it  is  a  Secondary  or  Inverse 
Pyramidal  or  Inverse  Octahedral  Plane,  or  a  Pyra- 
midal Plane  of  the  Second  Order.     If  it  cuts  the  two 
lateral  axes  unequally,  it  is  a  Ditetragonal  Pyramidal 
Plane,  or  a  Zirconoidal  Plane,  or  a  Dioctahedral  Plane. 

IV.  In  case  there  are  present  only  one-half  as  many 
faces  as  the  complete  form  should  have,  give  to  the 
partial  form  the  name  that  belongs  to  the  hemihedral 
form  having  the  same  parameters. 

HOLOHEDRAL    FORMS 

The  majority  of  forms  in  this  system  are  holohedral. 


64  ^OTES    ON    CRYSTALLOGRAPHY. 

They  are  distinguished  by  the  possession  of  five  planes, 
five  axes,  and  one  centre  of  symmetry. 

Of  the  axes  of  symmetry,  one  is  an  axis  of  tetragonal 
symmetry  and  the  four  others  are  axes  of  binary  sym- 
metry. 

Of  the  planes  of  symmetry  one  is  passed  midway  be- 
tween the  opposite  ends  of  the  unequal  extension,  par- 
allel to  the  lateral  axes  and  bisecting  the  vertical  axis. 
Two  of  the  other  planes  of  symmetry  pass  through  the 
vertical  axis  and  the  two  lateral  ones.  Two  more 
planes  of  symmetry  pass  through  the  vertical  axis  in 
such  a  way  as  to  form  an  angle  of  45°  with  each  of  the 
lateral  axes. 

The  axis  of  tetragonal  symmetry  joins  the  opposite 
ends  of  the  unequal  extension,  and  is  coincident  with 
the  vertical  axis. 

Of  the  axes  of  binary  symmetry,  two  are  coincident 
with  the  lateral  axes.  The  other  two  lie  in  the  plane 
of  the  lateral  axes,  but  form  angles  of  45°  with  them. 

In  the  simple  forms  the  Primary  and  Secondary 
Tetragonal  Prisms  are  identical  in  appearance,  and 
we  can  call  such  simple  forms  Primary  or  Secondary, 
as  we  chose.  It  is  customary,  however,  to  call  such 
simple  forms  Primary,  and  place  the  lateral  axes 
accordingly.  When  the  forms  are  compound,  then 
the  position  of  the  axes  of  the  selected  dominant  form 
determines  whether  the  subordinate  prisms  are  Pri- 
mary or  Secondary. 


THE    TETRAGONAL    SYSTEM.  65 

The  above  can  be  said  also  for  the  Primary  and 
Secondary  Pyramids. 

It  is  obvious  that  there  can  be  as  many  Primary 
and  Secondary  Pyramids  upon  a  single  crystal  as 
there  can  be  different  positions  on  the  vertical  axis  at 
which  planes  can  cut  that  axis — or  we  might  say, 
theoretically,  an  infinite  number ;  yet  we  find  practic- 
ally only  one,  two,  or  three,  or,  at  most,  a  very  few 
pyramids. 

HEMIHEDRAL    FORMS 

The  hemihedral  forms  of  the  Tetragonal  System 
that  are  important  to  Mineralogists  can  conveniently 
be  divided  into  two  groups,  the  Sphenoidal  and  the 
Pyramidal ;  but  for  crystallographic  reasons,  attention 
needs  to  be  called  also  to  the  Trapezohedral  Group. 

I.  The  Sphenoidal  Group  is  characterized  by  the 
wedge-shape  of  its  forms,  by  the  equality  of  two  of 
their  dimensions,  and  by  the  inequality  of  the  third 
dimension  compared  with  the  two  others. 

Attention  is  called  to  two  special  forms  in  this 
group,  the  Sphenoid  and  the  Tetragonal  Scaleno- 
hedron. 

1.  The  Sphenoid  in  this  system  is  similar  to  that  in 
the  Orthorhombic  System,  except  that  two  of  the 
dimensions  of  the  former  are  equal,  while  all  three  of 
the  latter  are  unequal.  The  sphenoids  are  further 
distinguished  by  the  fact  that  their  four  faces  are 
5 


66  NOTES    ON    CRYSTALLOGRAPHY. 

composed  of  isosceles  triangles,  while  those  of  the 
Orthorhombic  sphenoids  are  composed  of  scalene  tri- 
angles. See  Figs.  192-195. 

As  in  the  Orthorhombic  System,  we  can  consider 
these  forms  to  have  been  produced  by  the  obliteration 
of  four  alternate  planes  of  the  tetragonal  or  square 
pyramid,  and  by  the  prolongation  of  the  other  four 
alternate  planes  until  they  meet  and  make  a  complete 
form.  See  Fig.  236,  whose  blackened  planes  indicate 
the  faces  suppressed.  For  the  purpose  of  distinction 
these  sphenoids  are  often  called  Tetragonal  Sphenoids. 
See  Fig.  194. 

2.  The  Tetragonal  Scalenohedron  can  be  considered 
to  have  been  formed  by  the  suppression  of  four  alter- 
nate pairs  of  planes  in  the  ditetragonal  pyramid,  and 
by  the  extension  of  the  other  four  alternate  pairs  of 
planes,  until  they  meet  and  make  a  complete  form. 
See  Fig.  237,  in  which  the  blackened  planes  indicate 
the  planes  suppressed.     The  resulting  form  has  eight 
faces  composed  of  scalene  triangles,  but  the  cutting 
edge  of  the  wedge  is  broken,  and  is  composed  of  two 
straight  lines  meeting  at  an  angle.     See  Figs.  196  and 
197.     In  the  sphenoids  the  cutting  edge  is  formed  by  a 
single  straight  line.     See  Figs.  192-194. 

3.  The  symmetry  in  the  Sphenoid  and  in  the  Tetra- 
gonal Scalenohedron  is  lower  than  that  of  the  holohe- 
dral  forms.     In  the  Sphenoidal  Group  there  are  two 


THE    TETRAGONAL    SYSTEM.  67 

vertical  planes  of  symmetry  that  form  angles  of  45° 
with  the  lateral  axes.  There  are  also  three  axes  of 
binary  symmetry  coincident  with  the  three  crystallo- 
graphic  axes.  There  is  no  centre  of  symmetry.  See 
Figs.  192-197. 

II.  The  Pyramidal  Group  comprises  only  two  dis- 
tinct forms  of  importance  in  our  work  :  the  Henri- Di- 
tetragonal  Prisms,  or  Tertiary  Prisms,  or  Prisms  of  the 
Third  Order;  and  the  Hemi-Ditetragonal  Pyramids,  or 
Tertiary  Pyramids,  or  Pyramids  of  the  Third  Order. 

1.  The  Hemi-Ditetragonal   or  Tertiary   Prism  or 
Prism  of  the  Third  Order  can  be  regarded  as  formed 
by  the  suppression  of  each  alternate  face  of  the  di- 
tetragonal  prism  and  by  the  extension  of  the  other 
four  faces  until  they  meet,  forming  a  four-faced  prism. 
This  prism  is  found  as  a  modifying  form  only.      See 
Fig.  238,  in  which  the  shaded  faces  indicate  the  oblit- 
erated planes. 

2.  The  Hemi-Ditetragonal  or  Tertiary  Pyramid  or 
Pyramid  of  the  Third  Order  can   be  considered  as 
formed  by  the  suppression  of  alternate  planes  on  the 
upper  half  of  the  ditetragonal  pyramid,   and  a  like 
suppression  of  the  similar  planes  directly  below.    Then 
the  set  of  eight  corresponding  faces  are  extended  until 
they  meet,  completing  the  form  and  developing  an 
eight-sided  pyramid  similar  to  the  primary  and  sec- 
ondary pyramids  or  to  those  of  the  first  and  second 


68  NOTES    ON    CRYSTALLOGRAPHY. 

order.  See  Fig.  239,  whose  shaded  planes  indicate 
the  faces  suppressed. 

Both  of  the  above  forms  can  be  distinguished  by  de- 
termining the  parameters  of  the  planes,  and  observing 
that  the  number  of  planes  is  one-half  those  required 
by  the  corresponding  holohedral  form.  The  Tertiary 
Pyramid  or  Pyramid  of  the  Third  Order,  like  the 
Tertiary  Prism  or  Prism  of  the  Third  Order,  never 
occurs  except  as  a  modifying  form.  If  either  of  the 
above  forms  occurred  alone  as  a  simple  form,  it  would 
be  identical  with  a  Primary  or  Secondary  Prism  or 
Pyramid.  The  different  position  of  the  lateral  axes 
is  the  only  distinguishing  feature,  and  this  can  be  ob- 
served only  in  compound  forms.  See  Figs.  198  and 
199. 

Fig.  198  shows  a  cross-section  of  the  primary  prism 
or  primary  pyramid  inscribed  in  a  cross-section  of  a 
tertiary  prism  or  pyramid.  This  figure  illustrates  the 
different  positions  of  the  lateral  axes  for  the  different 
prisms  and  pyramids  when  in  compound  forms,  as 
shown  in  Fig.  199. 

3.  The  symmetry  of  the  Pyramidal  Group  is  still 
lower  than  that  of  the  Sphenoidal  Group.  The  former 
has  one  plane  of  symmetry,  a  single  axis  of  tetragonal 
symmetry,  and  a  centre  of  symmetry.  The  plane  of 
symmetry  lies  in  the  plane  of  the  lateral  axes  and 
bisects  the  vertical  axis.  The  axis  of  tetragonal  sym- 


THE   TETRAGONAL   SYSTEM.  69 

raetry  is  coincident  with  the  vertical  axis  and  there- 
fore is  perpendicular  to  the  plane  of  symmetry. 

III.  The  Trapezohedral  Group  or  the  Tetragonal 
Trapezohedrons  are  discussed  here  to  some  extent 
because  they  are  common  in  the  larger  sets  of  crystal 
models.  These  forms  are  not  known  to  occur  in 
any  natural  minerals,  but  only  in  artificial  crys- 
tallizations. They  can  be  considered  to  be  formed 
by  the  extension  of  the  alternate  planes  of  the  dite- 
tragonal  pyramid  above  and  below,  until  they  meet, 
(see  Fig.  184).  This  gives  rise  to  two  forms  called 
respectively  Right-handed  (r)  and  Left-handed  (Q,  or 
Positive  and  Negative.  See  Figs.  200  and  201. 

The  Trapezohedrons  have  four  axes  of  binary  sym- 
metry lying  in  the  plane  of  the  lateral  axes,  and  have 
one  axis  of  tetragonal  symmetry  that  coincides  with 
the  vertical  axis. 

COMPOUND   FORMS 

The  common  forms  of  the  Tetragonal  System  are 
holohedral  ones,  which  are  sometimes  combined  with 
hemihedral  forms.  See  Fig.  240.  Of  the  hemihedral 
forms  the  sphenoids  alone  occur  in  crystals  separated 
from  other  forms.  See  Figs.  192-194,  196,  and  197. 

READING   DRAWINGS    OF   TETRAGONAL   CRYSTALS 

Since  the  lengths  of  the  two  lateral  axes  are  the 
same,  one  letter  will  suffice  to  designate  both  semi- 


70  NOTES    ON    CRYSTALLOGRAPHY. 

lateral  axes,  a.  For  the  vertical  semi-axis  the  usual 
symbol  is  employed,  c.  The  symbols  of  a  simple 
prism  in  this  system  are,  in  the  Weiss  notation, 
a  :  a  :  oo  c,  or  as  it  is  very  commonly  written  a  :  a  :  oo  c, 
with  the  omission  of  the  vertical  mark.  Naumann's 
notation  for  this  prism  is  oo  P,  Dana's,  I  or  m,  and  Mil- 
ler's, 110. 

The  various  notations  are  correlated  for  the  forms  in 
Table  IV  and,  so  far  as  may  be,  on  the  Figs.  41-44 
and  151-201. 


THE   TETRAGONAL   SYSTEM. 


71 


TABLE   IV 

TETRAGONAL  FORMS  AND  NOTATIONS 


Forms. 

Weiss. 

Naumann. 

Dana. 

Miller. 

Basal  Pinacoids. 

oca  :  aoa  :  c 

OP 

Oor  c 

001 

Primary  Prisms. 

a  :  a  :  ooc 

ooP 

Jor  m 

110 

Secondary  Prisms. 

a  :  QO  a  :  oo  c 

00  P  00 

i-i  or  a 

100 

Ditetragonal 
Prisms. 

a:  na  :  QOC 

oo  Pn 

i-n 

hlcQ 

Primary  Pyramids. 

a  :  a  :  c 
a  :  a  :  me 

P 

mP 

1 

m 

111 

hhl 

Secondary 
Pyramids. 

a  :  ooa  :  c 
a  :  QO  a  :  me 

Poo 

mPoo 

l-« 

m-i 

101 

hQl 

Ditetragonal 
Pyramids. 

a  :  na  :  me 

mPn 

m-n 

hkl 

Tetragonal 
Sphenoids. 

i(a  :  a  :  me) 
—  Ka  •  a  "  wic) 

mP 
2 
mP 

m 
~2 
m 

K\hhl} 

K{hhl\ 

2 

~  2 

Tetragonal 
Scalenohedrons. 

i(a  :  na  :  me) 
—  £(a  :  na  :  me) 

mPn 

2~ 
mPn 
2 

(m-n) 
2 
(m-n) 

"~2~ 

K\hkl\ 

*\h&} 

fooPn"] 

i-n 

1  I  1  f\  I 

Tertiary  Prisms. 

£[a  :  na  :  oo  c] 

L    2    J 
TooPnl 

2 
i-n 

Tr^/iAcOf 

TTJ/lfcOf 

L    2    J 

2 

Tertiary  Pyramids. 

i[a  :  na  :  me] 
—  i[a  :  na  :  me] 

rmPnl 
L    2    J 
frnPn-] 

[m-n] 
~2~ 
[m-n] 

K{hkl\ 

K\hkl} 

L    2    J 

2 

mPn  „. 

m-n 

1   1.7  ll 

Tetragonal 
Trapezohedrons. 

i(a  :  na  :  mc)r 
—  i(a  :  na  :  me)  I 

2 
mPn  7 
•~~2~" 

"2    r 
m-7i  j 
~~  2 

T\hkl\ 

r{hkl\ 

72  NOTES    ON    CRYSTALLOGRAPHY. 

DIRECTIONS    FOR    STUDYING   TETRAGONAL    CRYSTALS 

1.  Prove  that  the  crystal  or  model  is  Tetragonal. 

2.  Locate  the  axes,  as  previously  directed. 

3.  Note  the  dominant  and  modifying  forms  in  the 
order  of  their  importance. 

4.  Select  and  name  the  planes  of  each  form  in  the 
following  order :  pinacoids,  prisms,  domes,  and  pyra- 
mids. 

5.  Distinguish  the  holohedral  and  hemihedral  forms, 
naming  the  sphenoids,  scalenohedrons,  tertiary  prisms 
and    pyramids,    and   the   trapezohedrons  when    they 
occur. 

6.  Locate  the  planes,  axes,  and  centres  of  symmetry. 


CHAPTER  VI 

THE    HEXAGONAL    SYSTEM 

IN  this  system  it  is  found  best,  as  a  matter  of  prac- 
tical convenience,  to  depart  from  the  custom  followed 
in  the  other  systems  of  using  three  axes,  and  to  em- 
ploy four.  Of  these  four,  three  are  taken  as  Lateral 
Axes,  and  are  so  placed  that  they  form  angles  of  60° 
with  one  another.  The  fourth  axis,  like  the  Tetra- 
gonal vertical  axis,  is  either  longer  or  shorter  than  the 
lateral  axes,  and  is  perpendicular  to  them.  This  axis 
is  called,  as  in  the  other  systems,  the  Vertical  Axis. 
See  Fig.  6. 

The  Hexagonal  System  is  considered  in  connection 
with  the  Tetragonal  System,  because  it  has  one  dimen- 
sion that  is  either  longer  or  shorter  than  its  other 
dimensions,  which  are  equal  to  one  another ;  also 
because  the  end  planes  of  the  longer  or  shorter  direc- 
tion are  similar  to  one  another,  but  are  unlike  the 
planes  on  the  sides.  The  most  obvious  difference  in 
the  forms  is  that  the  Tetragonal  System  has  its  parts 
in  twos,  fours,  or  eights  (see  Figs.  41-44  and  154-201), 
while  the  Hexagonal  System  has  its  parts  in  threes, 

(73) 


74  NOTES    ON    CRYSTALLOGRAPHY. 

sixes,  or  some  multiple  of  three.     See  Figs.  36-40, 
45-50,  54,  55,  138-141,  202-234,  and  240-324. 

The  symmetries  of  the  holohedral  forms  in  the  two 
systems  are  similar,  as  the  Tetragonal  System  has  one 
horizontal  and  four  vertical  planes  of  symmetry  (see 
Figs.  41-44,  155,  157-159,  and  161-191),  while  the 
Hexagonal  System  has  one  horizontal  and  six  vertical 
planes  of  symmetry  (see  Figs.  36-40,  203-208,  254- 
267,  315-319,  and  321-323). 

Some  crystallographers,  e.  g.,  Miller  and  Schrauf, 
employ  three  axes  for  this  system,  while  others,  e.  g., 
Groth,  separate  the  Hexagonal  System  into  two  parts ; 
one  part  retains  the  old  name  of  the  Hexagonal  Sys- 
tem and  has,  like  it,  four  axes,  while  the  other  part  is 
designated  as  the  Rhombohedral  or  Trigonal  System 
and  has  only  three  axes. 

Liebisch  uses  the  four  axes  for  the  complete  system 
and  divides  it  into  two  grand  divisions  according  to 
the  grade  of  the  axis  of  symmetry  which  is  coincident 
with  the  vertical  axis.  When  the  vertical  axis  is  co- 
incident with  an  axis  of  hexagonal  symmetry,  the 
forms  are  placed  in  the  Hexagonal  Division.  When 
the  vertical  axis  is  coincident  with  an  axis  of  trigonal 
symmetry,  the  forms  are  placed  in  the  Rhombohedral 
(Trigonal)  Division.  The  same  divisions  are  made 
by  the  Danas  and  by  Moses. 

For  the  semi-axis  in  the  Hexagonal  System  we  use 


THE    HEXAGONAL    SYSTEM.  75 

in  the  Miller-Bravais  notation  the  following  indices 
(see  Fig.  6):  h  for  the  al  semi-axis ;  h  for  the  -al;  k 
for  the  a2;  k  for  the  -a2;  i  for  the  a3;  I  for  the  -a3;  I 
for  the  c1;  and  Z  for  the  -c. 

To  repeat,  the  Miller-Bravais  Indices,  then,  are  hkll, 
and  the  modernized  Weiss  Parameters  are  al:a2:-as: 
c,  or,  in  a  more  general  form,  nal:pa2:-a&:mc.  It  is, 
however,  customary  to  omit  the  subscript  figures,  since 
the  lateral  semi-axes  are  all  equal,  and  to  write  the 
notations  as  follows  :  na  :  pa  :  -a  :  me.  The  vertical 
mark  is  often  omitted  over  the  c,  as  it  is  in  the  Tetra- 
gonal System. 

NOMENCLATURE 

Owing  to  the  employment  of  the  four  axes  and  to 
the  diverse  grades  of  symmetry,  or  to  the  numerous 
and  important  partial  forms,  the  nomenclature  in  this 
system  is  more  complicated  than  in  the  Tetragonal  or 
even  in  the  Isometric  System.  To  a  considerable 
extent  the  forms  have  names  similar  to  those  of  the 
Tetragonal  System. 

RELATIONS    OF   PLANES   TO    AXES 

As  in  the  preceding  system,  the  axes  are  placed  so 
as  to  have  as  many  pinacoidal  and  prismatic  planes 
as  possible,  with  the  fewest  possible  pyramidal  planes. 
This  rule  extends  to  all  the  partial  as  well  as  to  the 
holohedral  forms. 


76  NOTES    ON    CRYSTALLOGRAPHY. 

DISTINGUISHING  CHARACTERISTICS    OF    HEXAGONAL 
CRYSTALS 

The  crystals  of  this  system  are  generally  distin- 
guished by  the  possession  of  three  equal  extensions 
and  one  unequal ;  by  the  fact  that  the  opposite  ends 
of  the  unequal  extension  are  similar  ;  and  by  the  fur- 
ther fact  that  the  planes  at  the  ends  of  the  unequal 
extension  are  commonly  in  threes  or  sixes  or  some 
multiple  of  three ;  or,  as  previously  stated,  the  vertical 
axis  (the  axis  of  unequal  extension)  is  coincident  with 
an  axis  of  hexagonal  or  trigonal  symmetry.  See  Figs. 
36-40,  45-50,  54,  55, 138-141,  202-234,  and  241-324. 

PRINCIPAL    FORMS    0F    THE    HEXAGONAL    SYSTEM 

As  a  matter  of  convenience  there  is  given  below  a 
summary  of  the  principal  forms  of  this  system,  or 
those  which  are  described  more  fully  later  in  the  text. 

I.  Holohedral  Forms : 

1.  Basal  Pinacoid. 

2.  Primary  Hexagonal  Prism. 

3.  Secondary  Hexagonal  Prism. 

4.  Dihexagonal  Prism. 

5.  Primary  Hexagonal  Pyramid. 

6.  Secondary  Hexagonal  Pyramid. 

7.  Dihexagonal  Pyramid. 


THE   HEXAGONAL    SYSTEM. 

II.  Hemihedral Forms: 

A.  Rhombohedral  Group : 

1.  Primary  Rhombohedron : 

a.  Positive. 

b.  Negative. 

2,  Hexagonal  Scalenohedron  : 

a.  Positive. 

b.  Negative. 

B.  Pyramidal  Group : 

1.  Tertiary  Hexagonal  Prism  : 

a.  Positive  or  Right-handed. 

b.  Negative  or  Left-handed. 

2.  Tertiary  Hexagonal  Pyramid  : 

a.  Positive  or  Right-handed. 

b.  Negative  or  Left-handed. 

C.  Trapezohedral  Group : 

1.  Hexagonal  Trapezohedron : 

a.  Positive  or  Right-handed. 

b.  Negative  or  Left-handed. 

D.  Trigonal  Group : 

1.  Ditrigonal  Pyramid: 

a.  Positive. 

b.  Negative. 

III.  Tetartohedral  Forms : 

A.  Rhombohedral  Group  : 

1.  Secondary  Rhombohedron  : 
a.  Positive : 


77 


78  NOTES    ON    CRYSTALLOGRAPHY. 

u.   Right-handed. 
w.  Left-handed. 
b.  Negative : 

x.  Right-handed. 
z.    Left-handed. 
2.  Tertiary  Rhombohedron : 

a.  Positive : 

u.   Right-handed. 
w.  Left-handed. 

b.  Negative : 

x.  Right-handed. 
z.    Left-handed. 
B.  Trapezohedral  Group  : 

1.  Secondary  Trigonal  Prism  : 

a.  Positive  or  Right-handed. 

b.  Negative  or  Left-handed. 

2.  Ditrigonal  Prism  : 

a.  Positive  or  Right-handed. 

b.  Negative  or  Left-handed. 

3.  Secondary  Trigonal  Pyramid  : 

a.  Positive : 

u.  Right-handed. 
w.  Left-handed. 

b.  Negative : 

x.  Right-handed. 
z.    Left-handed. 

4.  Trigonal  Trapezohedron : 


THE    HEXAGONAL    SYSTEM.  79 

a.  Positive : 

u.   Right-handed. 
w.  .Left-handed. 

b.  Negative : 

x.  Right-handed. 
z.    Left-handed. 
0.  Trigonal  Group  : 

1.  Primary  Trigonal  Prism  : 

a.  Positive. 

b.  Negative. 

2.  Tertiary  Trigonal  Prism : 

a.  Positive: 

u.  Right-handed. 
w.  Left-handed. 

b.  Negative : 

x.  Right-handed. 
z.  Left-handed. 

3.  Primary  Trigonal  Pyramid  : 

a.  Positive. 

b.  Negative. 

4.  Tertiary  Trigonal  Pyramid  : 

a.  Positive : 

u.  Right-handed. 
w.  Left-handed. 

b.  Negative : 

x.  Right-handed. 
z.  Left-handed. 


80  NOTES    ON    CRYSTALLOGRAPHY. 

IV.  Hemimorphic  Forms : 

1.  lodyrite  Type. 

2.  Nephelite  Type. 

3.  Tourmaline  Type. 

4.  Sodium-Periodate  Type. 

I.    HOLOHEDRAL  FORMS 

In  one  prominent  respect  the  Hexagonal  System 
differs  from  the  preceding  systems :  in  the  Hexagonal 
System  the  holohedral  forms  are  less  common  and 
important  than  are  the  hemihedral  forms. 

Following  as  closely  as  practicable  the  nomenclature 
of  the  Tetragonal  System,  we  find  that  the  holohedral 
planes  and  their  names  are  related  to  the  axes  as 
follows : 

1.  If  the  plane  is  parallel  to  the  lateral  axes,  it  is  a 
Pinacoid,  commonly  called  a  Basal  Pinacoid  or  a  Basal 
Plane.     Its  symbol  is  0  P  or  0001.     There  can  be  but 
two  such  planes  on  a  crystal,  the  same  as  in  the  Tet- 
ragonal System.     See  0  P  or  0001,  Figs.  37-39,  205- 
207,  215,  216,  220,  221,  242,  246-248,  263,  269,  272, 
275,  289,  and  315-323. 

2.  A  plane  parallel  to  the  vertical  axis  and  to  one 
of  the  lateral  axes,  and  cutting  the  other  two  lateral 
axes  at  equal  distances  from  the  centre  of  the  crystal, 
is  known  as  a  plane  belonging  to  a  Primary  Hexag- 
onal Prism  or  a  Hexagonal  Prism  of  the  First  Order. 
In  this  form  the  angles  of  the  lateral  edges  are  all 


THE   HEXAGONAL   SYSTEM.  81 

equal.  See  oo  P  or  1010,  Figs.  36-38, 40,  49,  202,  205, 
212-214,  217,  219,  254,  255,  283,  298,  302-304,  307- 
319,  and  321-323.  If  a  plane  is  parallel  to  the  verti- 
cal axis,  cuts  one  lateral  axis  at  some  unit  of  distance, 
and  intersects  the  other  two  lateral  axes  at  twice  that 
unit  of  distance,  it  is  said  to  be  a  plane  belonging  to  a 
Secondary  Hexagonal  Prism  or  a  Hexagonal  Prism 
of  the  Second  Order.  As  in  the  Primary  Prism,  the 
angles  of  the  lateral  edges  are  all  equal.  See  oo  P  2 
or  1120,  Figs.  46,  50,  206,  212,  215,  216,  220,  278- 
280,  299,  318-320,  322,  and  323.  If  the  plane  is 
parallel  to  the  vertical  axis,  but  cuts  all  three  lateral 
axes  at  unequal  distances,  then  the  plane  is  said  to 
belong  to  a  Dihexagonal  Prism.  In  this  form  the 
alternate  angles  of  the  lateral  edges  are  unequal.  See 
Figs.  207,  219,  242,  246,  and  257. 

3.  If  a  plane  cuts  the  vertical  axis,  is  parallel  to  one 
lateral  axis,  and  intersects  the  other  two  at  equal  dis- 
tances, the  plane  belongs  to  a  Primary  Hexagonal 
Pyramid  or  a  Hexagonal  Pyramid  of  the  First  Order. 
In  this  form  the  lateral  edges  are  straight  and  equal, 
while  the  edges  running  to  the  apices  form  equal 
angles.  See  htihl,  1011,  raP,  and  P,  Figs.  36-39,  47, 
202,  203,  212-214,  217-219,  254-266,  315,  316,  318, 
319,  and  321-323.  If  the  plane  cuts  the  vertical  axis 
and  intersects  one  lateral  axis  at  a  chosen  unit  of  dis- 
tance, and  the  other  two  lateral  axes  at  twice  that  unit 
6 


82  NOTES   ON   CRYSTALLOGRAPHY. 

of  distance,  it  is  a  plane  belonging  to  a  Secondary 
Hexagonal  Pyramid  or  a  Hexagonal  Pyramid  of  the 
Second  Order.  The  edges  and  angles  are  the  same 
as  in  the  Primary  Pyramid.  See  P2,  2P2,  raP2, 
hhZhl,  and  1122,  Figs.  37,  40,  204,  209,  212,  243,  249, 
255,  258,  261,  267,  276,  306,  308,  317,  319,  and  321- 
323.  If  the  plane  cuts  the  vertical  axis  and  intersects 
all  the  lateral  axes  at  unequal  distances,  it  belongs  to  a 
Dihexagonal  Pyramid.  The  lateral  edges  are  hori- 
zontal and  equal,  but  the  alternate  angles  formed  by 
the  edges  running  to  the  apices  are  unequal.  See 
htel,  mPn,  2133,  and  3Pf,  Figs.  40,  208,  219,  229, 
234,  241,  259,  262,  266,  and  321. 

4.  The  above  statements  apply  to  the  holohedral 
forms.  In  case  the  plane  is  found  to  belong  to  a 
partial  form,  then  the  special  name  of  the  partial  form 
having  the  same  parameters  should  be  used. 

The  Primary  Hexagonal  Prism  and  Pyramid  pos- 
sess cross-sections  as  shown  in  Fig.  202,  which  indi- 
cates the  relation  of  the  lateral  axes  to  the  planes. 

When  the  Secondary  Hexagonal  Prism  or  Pyramid 
is  in  a  simple  form,  its  appearance  is  identical  with 
that  of  the  Primary  Hexagonal  Prism  or  Pyramid. 
We  may  call  these  simple  forms  either  Primary  or 
Secondary,  as  we  prefer,  although  it  is  customary 
always  to  call  the  simple  forms  Primary,  as  in  the 
case  of  the  Tetragonal  System.  See  Figs.  36-40,  202- 


THE    HEXAGONAL    SYSTEM.  83 

206,  212,  218,  243,  249,  254,  264,  268,  315-318,  and 
323. 

When  the  forms  are  compound,  then  the  position  of 
the  axes  of  the  dominant  form  determines  whether 
the  subordinate  forms  are  Primary  or  Secondary. 
See  Figs.  36-40,  254-267,  and  308-323. 

As  in  the  Tetragonal  System,  we  can  have  as  many 
Primary  and  Secondary  Pyramids  as  we  can  have  dif- 
ferent points  on  the  vertical  axis.  That  is,  we  can 
have,  theoretically,  an  indefinite  number ;  practically 
we  find  but  few  on  any  crystal.  See  Figs.  36-40, 
254-267,  and  308-323. 

A  student  naturally  desires  to  know  why,  in  the 
case  of  the  Secondary  Prisms  and  Pyramids,  we  state 
that  the  planes  cut  two  lateral  axes  at  twice  the  unit 
of  distance  at  which  it  cuts  the  other  one. 

The  reason  is  shown  by  a  simple  trigonometric  opera- 
tion. See  Fig.  209.  From  Geometry  we  know  that 
the  side  of  a  regular  hexagon  inscribed  in  a  circle  is 
equal  to  the  radius  of  that  circle.  This  makes  the  side 
(d)  of  the  hexagon  and  the  two  radii  (b  and  g)  equal. 
Since,  then,  the  triangle  formed  by  the  sides  b,  d,  and  s 
is  an  equilateral  one,  it  follows  according  to  Geometry 
that  the  angles  are  all  equal.  The  sides  b  and  d  of  the 
triangle  are  the  semi-axes  in  a  section  of  a  primary 
hexagonal  prism  or  pyramid.  See  Fig.  202.  There- 
fore the  angle  b  p  d  is  an  angle  of  60°,  and  hence  the 


84  NOTES   ON    CRYSTALLOGRAPHY. 

other  two  angles  of  the  triangle  are  angles  of  60°. 
From  Trigonometry  we  learn  that  u  r  is  the  tangent  of 
the  angle  b  p  d  or  60°.  Trigonometry  also  teaches  us 
that  Tan.  60°  =  1/3.  From  Geometry  we  know  that 
(pr)2  =  b2  +  (ur)2.  Now  b  is  the  shorter  axis  or  the 
smaller  parameter  of  the  secondary  prism  or  pyramid  ; 
therefore,  in  Crystallography  it  is  unity  or  1  ;  while  u  r 
is  the  tangent  of  60°  or  1/3.  Hence  by  substituting 
these  numbers  our  equation  reads  :  (pr)2  =  1 2  -f  (1/3) 2, 
or  pr  =  1/1  +  3  =1/4  =  2.  Now  the  2  thus  obtained 
is  one  of  the  longer  parameters  of  the  secondary  prism 
or  pyramid.  From  inspection  of  Fig.  209  it  can  be 
seen  that  both  the  longer  parameters  are  the  same ; 
hence  it  follows  that  in  the  Weiss  notation  the  para- 
meters of  a  secondary  prism  would  be  2a  :  —  a  :  2a  : 
oo  c,  and  those  of  a  secondary  pyramid  would  be  2a  :  — 
a  :  2a  :  me. 

The  holohedral  forms  possess  six  vertical  planes  of 
symmetry  :  three  are  coincident  with  the  vertical  axis 
and  the  three  lateral  axes ;  the  other  three  coin- 
cide with  the  vertical  axis,  but  bisect  the  angles 
between  the  lateral  axes.  Further,  there  is  one  hori- 
zontal plane  of  symmetry  which  bisects  the  vertical 
axis  and  lies  in  the  plane  of  the  lateral  axes. 

Again,  the  holohedral  forms  have  six  horizontal 
axes  of  binary  symmetry  :  three  that  bisect  the  angles 
between  the  lateral  axes,  and  three  that  are  coincident 


THE    HEXAGONAL    SYSTEM.  85 

with  those  crystal  axes.  These  forms  have  also  a 
vertical  axis  of  hexagonal  symmetry  which  is  coinci- 
dent with  the  vertical  crystal  axis,  as  well  as  a  centre 
of  symmetry. 

II.    HEMIHEDRAL    FORMS 

A.  Rhombohedral  Group.  The  distinctive  forms  in 
this  group  are  two : 

1.  The  Rhombohedron. 

2.  The  Scalenohedron. 

1.  The  Rhombohedron  as  a  hemihedral  form  can  be 
considered  to  be  produced  by  the  suppression  of  the 
alternate  upper  and  lower  planes  of  the  primary  hex- 
agonal pyramid  and  by  the  extension  of  the  other  al- 
ternate planes  until  they  meet  one  another  so  as  to 
produce  a  complete  form.  See  Figs.  218  and  233.  In 
Fig.  218,  if  the  shaded  planes  are  the  ones  considered 
suppressed,  the  rhombohedron  produced  by  the  exten- 
sion of  the  non-shaded  planes  until  they  meet  is  called 
a  Positive  Rhombohedron.  See  Fig.  139. 

A  rhombohedron  is  called  Positive  when  one  of  its 
three  upper  rhombs  stands  face  to  face  with  the  ob- 
server. 

When  the  shaded  parts  of  the  primary  hexagonal 
pyramid  (Fig.  218)  are  the  parts  carried  out  until  they 
meet,  and  the  non-shaded  parts  are  the  parts  obliter- 
ated, then  the  rhombohedron  produced  is  known  as  a 
Negative  Rhombohedron.  See  Fig.  138. 


86  NOTES    ON    CRYSTALLOGRAPHY. 

A  rhombohedron  is  called  Negative  when  one  of  the 
three  upper  edges  is  turned  directly  towards  the  ob- 
server ;  or  in  other  words,  when  this  edge  lies  in  the 
plane  of  symmetry  bisecting  the  observer. 

Besides  the  six  equal  and  similar  rhombs  that  bound 
the  rhombohedron,  it  possesses  two  kinds  of  edges  and 
two  kinds  of  solid  angles.  There  are  six  similar 
Terminal  Edges,  three  above  and  three  below,  which 
are  marked  in  Figs.  138  and  139  by  the  letter  A.  The 
junction  of  each  set  of  three  terminal  edges  marks  each 
end  of  the  vertical  axis.  Again,  there  are  six  equal 
and  similar  Lateral  Edges,  which  run  zigzag  about  the 
crystal  and  which  are  designated  by  the  letter  B,  in 
the  same  figures. 

At  each  end  of  the  vertical  axis  there  is  a  solid  angle 
formed  by  three  equal  plane  angles.  These  two  solid 
angles  are  designated  on  the  figures  by  the  letter  C. 
Further,  the  rhombohedrons  have  six  lateral  solid 
angles,  designated  by  the  letter  D.  While  these  lateral 
angles  are  similar,  they  are  not  formed  by  the  inter- 
section of  equal  plane  angles,  but  by  either  two  obtuse 
angles  and  one  acute  angle,  or  by  one  obtuse  angle 
and  two  acute  angles.  The  angles  measured  over  the 
lateral  edges  are  all  alike,  but  are  different  from  the 
angles  measured  over  the  terminal  edges.  If  the  angle 
obtained  by  measuring  over  a  terminal  edge  is  added 
to  the  angle  obtained  by  measuring  over  a  lateral  edge, 


THE    HEXAGONAL    SYSTEM.  87 

the  sum  of  the  two  is  180°  ;  or  one  is  as  much  greater 
than  a  right  angle  as  the  other  is  less.  Hence  it  is 
customary  to  place  the  rhombohedrons  in  two  sections, 
Acute  and  Obtuse. 

An  Acute  Rhombohedron  is  one  whose  equal  angles 
measured  over  the  terminal  edges  are  each  less  than 
90°.  See  Fig.  222. 

An  Obtuse  Rhombohedron  is  one  whose  equal  angles 
measured  over  the  terminal  edges  are  each  greater 
than  90°.  See  Fig.  223. 

It  often  happens  that,  upon  a  crystal,  several 
different  rhombohedrons  occur,  which  have  the  same 
intercepts  upon  the  lateral  axes,  but  have  different 
intercepts  upon  the  vertical  axis.  In  such  a  case  one 
is  selected  as  the  Principal  or  Fundamental  Rhombo- 
hedron, while  the  others  are  considered  as  Subordinate 
Rhombohedrons.  See  Figs.  45,  224-228,  270,  271, 
275-277,  280,  and  307-314. 

Having  selected  the  principal  rhombohedron,  we  find 
that  all  rhombohedrons  which  have  the  same  lateral 
parameters,  but  which  have  larger  intercepts  on  the 
vertical  axis,  are  acute  rhombohedrons,  but  that  if  they 
have  smaller  intercepts  on  the  vertical  axis,  they  are 
obtuse  rhombohedrons.  See  Figs.  224-227,  275-277, 
280,  and  286. 

It  is  found  that  these  rhombohedrons  have  this  rela- 
tion to  one  another :  A  positive  rhombohedron  will 


88  NOTES    ON    CRYSTALLOGRAPHY. 

truncate  the  terminal  edges  of  the  negative  rhombo- 
hedron  that  has  twice  its  parameter  on  the  vertical 
axis.  Again,  a  negative  rhombohedron  will  truncate 
the  terminal  edges  of  the  positive  rhombohedron  that 
has  twice  its  parameter  on'the  vertical  axis.  See  Figs. 
45,  225,  and  228. 

The  vertical  axis,  as  before  stated,  joins  the  trihedral 
solid  angles,  while  the  three  lateral  axes  join  the  cen- 
tres of  the  opposite  lateral  zigzag  edges. 

The  rhombohedrons  thus  far  described  are  often 
designated  as  Primary  Rhombohedrons  or  as  Rhombo- 
hedrons of  the  First  Order. 

2.  The  Hexagonal  Scalenohedron  as  a  hemihedral 
form  of  the  Hexagonal  System  is  regarded  as  being 
formed  by  the  suppression  of  alternate  pairs  of  adja- 
cent planes  above  and  alternate  pairs  of  adjacent 
planes  below ;  and  by  the  extension  of  the  remaining 
pairs  of  planes  of  the  dihexagonal  pyramid  until  they 
meet  and  form  a  complete  figure.  This  is  illustrated 
in  Fig.  229,  in  which  the  extended  faces  are  shaded. 
See  also  Fig.  232,  in  which  we  have  the  scalenohedral 
faces  extended  to  complete  the  form.  The  pyramidal 
faces  used  are  marked  -J-,  and  the  suppressed  faces 
marked  — .  The  result  of  extending  the  shaded  faces 
in  Fig.  229  is  to  produce  a  form  bounded  by  twelve  sim- 
ilar Scalene  triangles ;  hence  its  name.  See  Fig.  140. 

If  we  also  extend  the  non-shaded  pairs  of  planes 


THE    HEXAGONAL    SYSTEM.  89 

and  suppress  the  others,  we  obtain  a  similar  form  as 
shown  in  Fig.  141.  The  first  form  is  called  Positive, 
and  the  second  Negative. 

The  Hexagonal  Scalenohedron  is  called  Hexagonal 
to  distinguish  it  from  the  Tetragonal  Scalenohedron ; 
but  as  the  latter  is  so  rare  and  is  never  found  except 
in  combination,  it  is  customary  to  speak  of  the  hexa- 
gonal form  as  the  Scalenohedron,  and  when  mentioning 
the  tetragonal  form,  to  designate  it  always  as  the 
Tetragonal  Scalenohedron.  See  Figs.  196  and  197. 

The  Hexagonal  Scalenohedron  has  six  lateral  edges 
above  and  six  lateral  edges  below  ;  and  their  terminal 
junctions  mark  the  two  ends  of  the  vertical  axis. 
The  angles  measured  over  the  lateral  edges  are  of  two 
kinds — alternately  acute  and  obtuse.  The  acute  angles 
above  are  over  the  obtuse  angles  below  ;  and  the  ob- 
tuse angles  above  are  over  the  acute  angles  below.  See 
Figs.  140,  141,  230-232,  244,  245,  252,  253,  and  287- 
305. 

The  Scalenohedron  has  six  equal  lateral  edges  that 
zigzag  about  the  crystal  ;  while  the  saw  teeth  produced 
have  equal  sides,  and  are  bisected  by  the  lateral  edges 
forming  the  obtuse  angles.  See  Figs.  140,  141,  232, 
244,  245,  252,  and  253. 

The  selection  of  the  Positive  and  Negative  forms  is 
an  arbitrary  matter,  although  much  depends  upon  the 
other  forms  with  which  they  are  combined. 


90  NOTES    ON    CRYSTALLOGRAPHY. 

It  is  customary  to  consider  a  scalenohedron  positive 
when  it  is  so  placed  that  the  terminal  edge  next  the 
observer  is  obtuse,  and  when  the  saw  tooth,  bisected  by 
the  terminal  edge,  has  its  point  downwards.  See  Figs. 
140  and  253. 

When  the  terminal  edge  next  to  the  observer  is 
acute  and  the  point  of  the  saw  tooth  is  turned  upwards, 
the  scalenohedron  is  negative.  See  Figs.  141  and  252. 

It  can  be  seen  that  the  zigzag  edges  of  the  rhombo- 
hedron  correspond  to  the  zigzag  edges  of  the  scaleno- 
hedron ;  therefore,  a  rhombohedron  can  be  inscribed 
in  any  scalenohedron  which  has  a  longer  vertical  axis 
than  has  the  rhombohedron.  The  rhombohedron 
thus  inscribed  is  known  as  the  Inscribed  Rhombo- 
hedron or  the  Rhombohedron  of  the  Middle  Edges. 
See  Fig.  231. 

The  vertical  axis  of  the  scalenohedron  is  the  pro- 
longed vertical  axis  of  the  inscribed  rhombohedron. 
Hence  there  may  be  an  indefinite  number  of  scaleno- 
hedrons  for  every  inscribed  rhombohedron  ;  but  in 
practice,  it  is  found  that  the  vertical  semi-axis  of  the 
scalenohedron  is  always  some  simple  multiple  of  the 
inscribed  rhombohedron. 

The  Rhombohedral  Group  has  three  vertical  planes 
of  symmetry,  which  bisect  the  angles  made  by  the 
lateral  axes  and  coincide  with  the  vertical  axis.  The 
group  has  also  three  horizontal  axes  of  binary  sym- 


THE   HEXAGONAL   SYSTEM.  91 

metry,  which  are  coincident  with  the  lateral  axes.     It 
has  also  one  vertical  axis  of  trigonal  symmetry,  which 
coincides  with  the  vertical  crystal  axis ;  and  a  centre 
of  symmetry. 
B.  The  Pyramidal  Group  : 

1.  Tertiary  Hexagonal  Prism : 

a.  Positive  or  Right-handed. 

b.  Negative  or  Left-handed. 

2.  Tertiary  Hexagonal  Pyramid : 

a.  Positive  or  Right-handed. 

b.  Negative  or  Left-handed. 

1.  The  Tertiary  Hexagonal  Prism  or  Prism  of  the 
Third  Order,  taken  as  a  hemihedral  form,  can  be  con- 
sidered to  be  produced  by  the  suppression  of  each  alter- 
nate plane  of  the  dihexagonal  prism  and  by  the  ex- 
tension of  the  sides  of  the  remaining  alternate  planes 
until  they  meet.  See  Figs.  213,  219,  and  242.  The 
form  thus  produced  is  identical  in  appearance  with  the 
Primary  and  Secondary  Hexagonal  Prisms,  and  it  dif- 
fers only  in  the  positions  of  the  lateral  axes.  A  hex- 
agonal prism  will  be  considered  a  Tertiary  Hexagonal 
Prism,  only  when  its  relation  to  the  other  forms  and  to 
the  selected  lateral  axes  shows  that  it  cuts  all  three 
lateral  axes  unequally.  This  fact  can  readily  be  seen 
when  a  Tertiary  Hexagonal  Prism  is  united  as  a  sub- 
ordinate form  with  a  dominant  Primary  or  Secondary 
Prism,  especially  if  there  are  a  number  of  other  sub- 
ordinate forms. 


92  NOTES    ON    CRYSTALLOGRAPHY. 

By  alternating  the  planes  that  we  consider  sup- 
pressed and  those  that  we  regard  as  extended,  two 
prisms  can  be  obtained  which  are  called  Positive  or 
Right-handed  and  Negative  or  Left-handed. 

In  the  above  cases,  when  the  positive  or  negative 
sign  is  employed,  the  sign  for  the  right-handed  or  left- 
handed  forms  is  omitted.  So,  when  the  r  or  I  is  used, 
the  positive  or  negative  sign  is  dropped.  This  is  the 
custom  in  all  cases  where  the  positive  or  negative,  or 
right-handed  or  left-handed,  symbols  are  employed.  -. 

In  giving  the  signs  on  the  figures  in  this  book,  es- 
pecially when  they  are  first  used,  both  the  positive  and 
the  right-handed,  or  the  negative  and  the  left-handed 
signs  are  given  in  order  to  impress  upon  the  student 
the  idea  that  either  sign  can  be  used  with  the  Naumaim 
symbols. 

2.  The  Tertiary  Hexagonal  Pyramid  can  be  re- 
garded as  formed  from  the  di hexagonal  pyramid  by 
the  extension  of  an  alternate  plane  above  and  its  ad- 
jacent plane  immediately  below,  (these  planes  stand 
base  to  base),  and  by  the  suppression  of  like  alternate 
pairs  of  planes.  See  Fig.  234. 

The  two  planes  in  each  case  would,  if  made  parallel 
to  the  vertical  axis,  unite  into  one  plane  coincident 
with  a  prism  plane. 

Two  sets  of  tertiary  pyramids  can  thus  be  formed  : 
Positive  or  Right-handed  and  Negative  or  Left-handed. 


THE   HEXAGONAL    SYSTEM.  93 

The  relation  of  the  Tertiary  Pyramid  to  the  Primary 
and  the  Secondary  Pyramids  is  the  same  as  previously 
stated  for  the  three  prisms. 

It  follows  from  what  has  been  previously  said  that 
neither  the  Tertiary  Prism  nor  the  Tertiary  Pyramid 
can  occur  except  in  combination  with  other  hexagonal 
forms. 

The  Tertiary  Hexagonal  Prisms  and  Pyramids  have 
an  axis  of  hexagonal  symmetry  that  is  coincident  with 
the  vertical  axis.  They  a'lso  possess  a  plane  of  sym- 
metry that  is  coincident  with  the  plane  of  the  lateral 
axes ;  and  a  centre  of  symmetry. 

C.  Trapezohedral  Group : 

1.  Hexagonal  Trapezohedron : 

a.  Positive  or  Right-handed. 

b.  Negative  or  Left-handed. 

The  Hexagonal  Trapezohedral  Group  does  not  oc- 
cur among  minerals,  but  is  met  with  in  artificial  crys- 
tals and  in  crystal  models. 

The  forms  of  this  group  can  be  considered  to  be 
produced  by  the  suppression  of  the  alternate  upper 
and  lower  planes  of  the  dihexagonal  pyramid  and  by 
the  extension  of  the  other  alternate  planes  until  they 
meet.  See  Fig.  241.  The  form  produced  is  a  twelve- 
faced  figure  with  unequal  zigzag  edges.  By  extend- 
ing the  planes  previously  suppressed  and  by  obliterat- 
ing the  planes  previously  extended,  another  form  is 


04  NOTES   ON   CRYSTALLOGRAPHY. 

produced,  which  is  similar  to  the  preceding  form,  just 
as  a  man's  left  hand  is  similar  to  his  right  hand. 
The  first  form  is  called  the  Positive  or  Right-handed 
Hexagonal  Trapezohedron  (see  Fig.  210);  and  the  sec- 
ond form  is  named  the  Negative  or  Left-handed- Hex- 
agonal Trapezohedron.  See  Fig.  211. 

The  Hexagonal  Trapezohedrons  have  no  plane  of 
symmetry,  but  they  have  six  horizontal  axes  of  binary 
symmetry,  (see  p.  84),  while  the  vertical  crystal  axis  is 
an  axis  of  hexagonal  symmetry. 

The  Hexagonal  Trapezohedron  can  be  distinguished 
from  other  forms  by  the  fact  that  its  planes  are  in 
sixes ;  by  the  fact  that  all  the  angles  formed  by  the 
edges  which  meet  at  the  apices  are  equal;  and  by  the 
further  fact  that  the  saw-teeth  of  its  zigzag  lateral 
edges  have  sides  of  unequal  length,  while  in  the  Hex- 
agonal Scalenohedron  the  zigzag  edges  have  the  sides 
of  the  saw-teeth  equal.  Further,  because  the  alternate 
zigzag  edges  in  the  Hexagonal  Trapezohedron  are  un- 
equal, it  happens  that  the  edge  angles  below  are  not 
directly  beneath  the  planes  above,  as  they  are  in  the 
Hexagonal  Scalenohedron,  but  are  thrown  to  one  side 
or  the  other.  Again,  the  faces  of  the  Hexagonal 
Trapezohedron  are  Trapeziums,  while  those  of  the  Hex- 
agonal Scalenohedron  are  Scalene  Triangles.  See  Figs. 
140,  141,  210,  211,  252,  and  253. 

The  right-handed  Hexagonal  Trapezohedrons  can 


THE    HEXAGONAL   SYSTEM.  95 

be  distinguished  from  the  left-handed  ones  in  the 
following  manner :  place  the  form  so  that  one  of  the 
edges  running  to  the  apex  will  be  directly  in  front  of 
the  observer  and  coincident  with  the  plane  of  sym- 
metry passing  between  his  eyes.  If  the  shorter  side  of 
the  zigzag  edge  immediately  in  front  inclines  to  the 
right-hand,  the  trapezohedron  is  right-handed ;  but 
if  the  shorter  side  is  inclined  towards  the  left-hand, 
the  trapezohedron  is  left-handed.  See  Figs.  210  and 
211. 

D.  Trigonal  Group : 

1.  Ditrigonal  Pyramid : 

a.  Positive. 

b.  Negative. 

Of  the  Trigonal  Group  the  only  form  to  which  at- 
tention is  called  here  is  the  Ditrigonal  Pyramid,  since 
the  other  Trigonal  forms  are  taken  up  elsewhere. 

This  form  as  a  hemihedral  form  is  considered  to  be 
produced  by  suppressing  the  alternate  pairs  of  planes 
above  and  below  of  the  dihexagonal  pyramid,  the  pairs 
of  planes  standing  base  to  base ;  and  by  extending  the 
corresponding  pairs  of  planes  above  and  below,  until 
the  form  is  completed.  See  Fig.  326,  in  which  the 
shaded  pairs  of  planes  denote  the  faces  suppressed, 
while  the  non-shaded  ones  are  the  pairs  of  planes 
extended.  Fig.  325  shows  the  resulting  form.  By 
varying  the  planes  to  be  suppressed  both  Positive  and 
Negative  forms  are  produced. 


96  NOTES   ON   CRYSTALLOGRAPHY. 

These  forms  possess  four  planes  of  symmetry  :  one 
is  horizontal  and  coincident  with  the  plane  of  the  lat- 
eral axes;  the  other  three  are  vertical  and  bisect 
the  angles  between  the  lateral  axes,  as  also  do  the 
three  axes  of  binary  symmetry.  The  vertical  axis  is 
an  axis  of  trigonal  symmetry. 

No  minerals  have  been  found  in  the  forms  of  this 
group. 

III.    TETARTOHEDRAL  FORMS 

A,  Rhombohedral  Group : 

1.  Secondary  Khombohedron : 

a.  Positive : 

u.  Right-handed, 
w.  Left-handed. 

b.  Negative : 

x.  Eight-handed. 
z.  Left-handed. 

2.  Tertiary  Rhombohedron : 

a.  Positive : 

u.  Right-handed. 
w.  Left-handed. 

b.  Negative : 

x.  Right-handed. 
z.  Left-handed. 

1.  The  Secondary  Rhombohedron  or  Rhombohedron 
of  the  Second  Order  can  be  regarded  as  obtained  by 
the  suppression  of  the  alternate  upper  and  lower  faces 
of  the  secondary  pyramid  and  the  extension  of  the 
others.  See  Fig.  243.  The  Secondary  Rhombohedron 


THE    HEXAGONAL    SYSTEM.  97 

differs  in  no  way  from  the  Primary  Rhombohedron 
except  in  the  position  of  the  axes.  Two  of  its  lateral 
indices  are  equal,  while  the  third  is  twice  as  great  as 
the  others.  The  Secondary  Rhombohedron  never  oc- 
curs alone,  but  is  always  found  in  combination  with 
other  forms,  the  positions  of  whose  axes  will  indicate 
the  nature  of  the  associated  rhombohedrons. 

By  alternation  of  the  planes  to  be  extended  and 
those  to  be  suppressed  two  Secondary  Rhombohedrons 
are  obtained :  Positive  and  Negative,  either  of  which 
may  be  Right-handed  or  Left-handed. 

2.  The  Tertiary  Rhombohedron  or  Rhombohedron 
of  the  Third  Order  can  be  considered  to  be  formed  by 
the  suppression  of  the  alternate  upper  and  lower 
planes  of  the  hexagonal  scalenohedron,  and  by  the  ex- 
tension of  the  other  alternate  planes  until  they  make 
a  completed  form.  Each  scalenohedron  will  produce 
two  forms,  and  since  there  are  two  hexagonal  scaleno- 
hedrons,  we  shall  have  four  Tertiary  Rhombohedrons. 
See  Figs.  244  and  245. 

The  Tertiary  Rhombohedron  differs  in  no  respect 
from  the  Primary  or  the  Secondary  Rhombohedron 
except  in  the  position  of  its  axes ;  but  as  it  is  always 
found  in  combination  with  other  forms,  the  position  of 
the  axes  of  the  latter  will  tell  whether  a  given  rhom- 
bohedral  plane  belongs  to  a  Primary,  Secondary,  or 
Tertiary  Rhombohedron.  Of  the  lateral  indices  of  the 
7 


98  NOTES    ON    CRYSTALLOGRAPHY. 

Tertiary  Rhombohedron,  one  is  unity,  one  twice,  and 
one  three  times  as  great. 

On  account  of  the  difference  in  the  position  of  their 
axes  the  Secondary  and  the  Tertiary  Rhombohedrons 
have  a  lower  order  of  symmetry  than  has  the  Primary 
Rhombohedron.  The  first  two  have  no  planes  of 
symmetry,  but  do  have  a  centre  of  symmetry  and  an 
axis  of  trigonal  symmetry  that  is  coincident  with  the 
vertical  axis  of  the  crystal. 

B.  Trapezohedral  Group : 

1.  Secondary  Trigonal  Prism : 

a.  Positive  or  Right-handed. 

b.  Negative  or  Left-handed. 

2.  Ditrigonal  Prism : 

a.  Positive  or  Right-handed. 

b.  Negative  or  Left-handed. 

3.  Secondary  Trigonal  Pyramid  : 

a.  Positive : 

u.  Right-handed. 
w.  Left-handed. 

b.  Negative : 

x.  Right-handed. 
z.  Left-handed. 

4.  Trigonal  Trapezohedron : 

a.  Positive : 

u.  Right-handed. 
w.  Left-handed. 

b.  Negative : 

x.  Right-handed. 
z.  Left-handed. 


THE    HEXAGONAL    SYSTEM.  99 

1.  The  Secondary  Trigonal  Prism  or  Trigonal  Prism 
of  the  Second  Order    can    be    considered    to    have 
been  produced  by  the  suppression  of  each  alternate 
plane  of  the  secondary  hexagonal  prism  and  the  ex- 
tension   of  the    other    three   faces   until   they  meet. 
Figure  220,  by  its  shading,  shows  the  planes  that  are 
supposed  to  be   suppressed  on   this  form,  while  the 
non-shaded   planes  are  those  supposed  to  be  extended. 
Figure  221  is  a  representation  of  the  form  produced. 

By  imagining  the  preceding  shaded  planes  of  the 
secondary  hexagonal  prism  extended  and  the  non- 
shaded  ones  suppressed,  another  Secondary  Trigonal 
Prism  will  be  produced.  One  prism  can  then  be  called 
the  Positive  or  Right-handed  and  the  other  the  Neg- 
ative or  Left-handed. 

2.  The  Ditrigonal  Prism  can  be  looked  upon  as  pro- 
duced by  the  extension  of  alternate  pairs  of  planes  of 
the  dihexagonal  prism  and  by  the  suppression  of  the 
other  alternate  pairs  of  planes.     As  before,  by  inter- 
changing the  planes  to  be  extended,  two  forms  are  pro- 
duced :  The  Positive  or  Right-handed  and  the  Negative 
or  Left-handed.     See  Figs.  219,  230,  and  246-248. 

3.  The  Secondary  Trigonal  Pyramid  is  regarded  as 
formed  from  the  secondary  hexagonal  pyramid  by  ex- 
tending the  three  alternate  planes  above  and  also  the 
three  alternate  planes  below,  whose  bases  are  coinci- 
dent with  the  bases  of  the  extended  planes  above.     The 


100  NOTES    ON    CRYSTALLOGRAPHY. 

other  alternate  planes  are  suppressed.  See  Fig.  249, 
in  which  the  shaded  planes  are  the  ones  that  are  here 
considered  suppressed. 

By  extending  the  planes  previously  considered  sup- 
pressed and  by  obliterating  the  others,  another  com- 
panion form  is  produced,  giving  us  Positive  or  Right- 
handed  and  Negative  or  Left-handed  Trigonal  Pyra- 
mids. See  Figs.  250  and  251. 

4.  The  Trigonal  Trapezohedron  can  be  looked  upon 
as  being  formed  by  the  extension,  in  the  scalenohe- 
dron,  of  every  other  plane  above  and  of  the  planes 
immediately  below  (i.  e.,  the  alternate  upper  and  lower 
planes  whose  bases  join),  and  by  the  suppression  of 
the  other  six  planes.  See  Figs.  252  and  253. 

By  alternating  the  planes  extended  and  those  sup- 
pressed, two  forms  can  be  produced  for  the  positive 
and  two  for  the  negative  scalenohedron,  or  four  in  all. 
These  are  designated  as  Positive  Right-  or  Left-handed, 
and  Negative  Right-  or  Left-handed.  See  Figs.  54 
and  55. 

The  Trigonal  Trapezohedrons  are  always  found  in 
combination  with  other  forms,  and  never  occur 


isolated  in  nature.      See  'J,   Figs.    308-312.     The 

group  possesses  three  axes  of  binary  symmetry  coin- 
cident with  the  lateral  axes,  and  an  axis  of  trigonal 
symmetry  coincident  with  the  vertical  axis,  but  it  has 
neither  plane  nor  centre  of  symmetry. 


THE    HEXAGONAL    SYSTEM.'  101 

C.  Trigonal  Group  : 

1.  Primary  Trigonal  Prism  : 

a.  Positive. 

s 

b.  Negative. 

2.  Tertiary  Trigonal  Prism  : 

a.  Positive : 

u.  Right-handed. 
w.  Left-handed. 

b.  Negative : 

x.  Right-handed. 
z.  Left-handed. 

3.  Primary  Trigonal  Pyramid  : 

a.  Positive. 

b.  Negative. 

4.  Tertiary  Trigonal  Pyramid  : 

a.  Positive: 

u.  Right-handed. 
w.  Left-handed. 

b.  Negative  : 

x.  Right-handed. 
z.  Left-handed. 

1.  The  Primary  Trigonal  Prism  can  be  considered  to 
be  produced  by  proceeding  with  the  primary  hexa- 
gonal prism  as  was  done  with  the  secondary  hexagonal 
prism  to  form  the  secondary  trigonal  prism.     See  page 
99.     Two  forms  result — Positive  and  Negative. 

2.  The  Tertiary  Trigonal  Prism  can  be  considered 
to  be  formed  by  extending  every  fourth  plane  of  the 
dihexagonal  prism  until  they  meet,  and  by  suppressing 
the  other  three-fourths.     By  varying  the  planes  ex- 
tended, four  forms  can  be  produced  :  Positive  Right- 


•102  NWES    ON    CRYSTALLOGRAPHY. 

and    Left-handed,   and    Negative  Right-   and   Left- 
handed. 

3.  The  Primary  Trigonal  Pyramid  as  a  tetartohe- 
dral   form   is   considered    to   be   produced    from   the 
primary  hexagonal  pyramid  in  the  same  way  in  which 
the  secondary  trigonal  pyramid  was  made.     See  page 
99.     Two  forms  result,  Positive  and  Negative-. 

4.  The  Tertiary  Trigonal  Pyramid  as  a  tetartohe- 
dral  form  can  be  regarded  as  produced  by  extending 
every  fourth  upper  and  lower  plane  (arranged  base  to 
base)  of  the  dihexagonal  pyramid  and  suppressing  the 
other  three-fourths.     By    varying  the    planes    to   be 
extended,  four  forms  result :  Positive  Right-  and  Left- 
handed,  and  Negative  Right-  and  Left-handed. 

These  trigonal  forms  have  one  horizontal  plane  of 
symmetry  coincident  with  the  plane  of  the  lateral 
axes,  and  an  axis  of  trigonal  symmetry  coincident 
with  the  vertical  axis,  but  are  destitute  of  any  centre 
of  symmetry. 

HEMIMORPHIC     FORMS. 

1.  The  lodyrite  Type  is  shown  in  Figs.  214-216. 

Fig.  214  is  terminated  at  one  end  by  a  hexagonal 
pyramid  (1011),  and  has  .upon  the  other  end  a  hexa- 
gonal prism  (lOlO),  and  a  basal  pinacoid  (OOOl). 
Figures  215  and  216  have  one  end  terminated  by  a 
basal  pinacoid  (0001)  and  a  pyramid  (4041),  and  the 
other  end  terminated  by  pyramids  (see  Fig.  215,  4045 


THE    HEXAGONAL    SYSTEM.  103 

and  9-9O8-20),*  or  by  a  pyramid  (see  Fig.  216,  4045). 
A  prism  (1120)  lies  between  the  terminal  pyramids. 

The  lodyrite  Type  has  six  vertical  planes  of  sym- 
metry, and  a  vertical  axis  of  hexagonal  symmetry 
coincident  with  the  vertical  axis. 

2.  The  Nephelite  Type  may  be  distinguished  by  the 
fact  that  the  terminations  at  opposite  ends  of  the  verti- 
cal axis  are  composed  of  different  hexagonal  pyramids, 
or  by  the  fact  that  the  crystal  is  formed  by  half  of  a 
hexagonal   pyramid    resting   on   its   basal    pinacoid. 
Figure  217  illustrates  well  one  of  the  first  set  of  forms. 
This  type  has  an  axis  of  hexagonal  symmetry. 

3.  The  Tourmaline  Type  is  most  commonly  repre- 
sented by  prisms,  terminated  at  each  end  by  diverse 
rhombohedrons.      These   forms    have   three   vertical 
planes  of  symmetry  that  bisect  the  lateral  axial  angles, 
and  an  axis  of  trigonal  symmetry  that  is  coincident 
with  the  vertical  crystal  axis.     See  Fig.  324. 

4.  The  Sodium  Periodate  Type  is  formed  by  taking 
the  upper  or  lower  part  of  a  trigonal  pyramid  and 
terminating  it  by  a  basal  pinacoid,  as  shown  by  Fig. 

*When,  as  occasionally  happens,  the  Miller-Bravais  indices  are  so 
large  that  a  single  index  contains  two  figures,  it  is  customary  to  avoid 
mistakes  in  the  indices  by  separating  each  index  by  a  point  at  the  tipper 
part  of  the  line.  See  above  and  11-2-T3-3  and  14'14-28'3.  Others  use 
the  points  below,  e.  g.,  10.5.6,  9.8.17.1,  and  7.4.11.6.  Others  em- 
ploy commas,  e.  g.,  6,4,10,4;  16.0,16,1;  and  9,9,18,20.  Still  others 
omit  all  points  of  separation. 


104  NOTES    ON    CRYSTALLOGRAPHY. 

327.  These  forms  have  one  vertical  axis  of  trigonal 
symmetry  coincident  with  the  vertical  crystallographic 
axis. 

COMPOUND    FORMS. 

The  compound  forms  of  the  Hexagonal  system  are 
numerous  and  varied.  Of  these  the  combinations  of 
the  hemihedral  and  tetartohedral  forms  are  more 
common  and  important  than  are  the  compound  holo- 
hedral  forms. 

The  student  should  take  especial  care  in  deciding 
which  is  the  principal  form  and  in  determining  the 
positions  of  its  axes,  since  upon  them  depends  the  ease 
or  difficulty  in  naming  the  subordinate  forms. 

References  to  the  figures  of  hexagonal  crystals  given 
in  this  book  will  show  that  the  majority  of  them  are 
compound,  and  that  some  are  more  or  less  compli- 
cated. See  Figs.  36-40,  45-50,  54,  55,  138-141,  202- 
234,  and  241-327. 

RULES    FOR    NAMING    HEXAGONAL    PLANES. 

I.  A  plane  parallel  to  all  the  lateral  axes  is  a  Basal 
Pinacoid  or  a  Basal  Plane. 

II.  A  plane  which  is  parallel  to  the  vertical  axis 
and  one  of  the  lateral  axes,  but  which  cuts  the  other 
two  lateral  axes  equally,  is  a  plane  belonging  to  a 
Primary  Prism: 

a.  If  the  number  of  similar  planes  is  six,  each  plane 
belongs  to  a  Primary  Hexagonal  Prism  or  Hexagonal 
Prism  of  the  First  Order. 


THE    HEXAGONAL    SYSTEM.  105 

b.  If  the  number  of  similar  planes  is  three,  each 
plane  belongs  to  a  Primary  Trigonal  Prism  or  Trigonal 
Prism  of  the  First  Order. 

III.  If  a  plane  is  parallel  to  the  vertical  axis  and 
cuts  one  lateral  axis  at  some  distance,  and  the  other 
two  lateral  axes  at  twice  that  distance,  the  plane  be- 
longs to  a  Secondary  Prism : 

a.  If  the  number  of  similar  planes  is  six,  each  plane 
belongs  to  a  Secondary  Hexagonal  Prism  or  Hexagonal 
Prism  of  the  Second  Order. 

b.  If  the  number  of  similar  planes  is  three,  each 
plane  belongs  to  a  Secondary  Trigonal  Prism  or  Tri- 
gonal Prism  of  the  Second  Order. 

IV.  If  the  plane  is  parallel  to  the  vertical  axis  and 
intersects  all  three  lateral  axes  at  unequal  distances, 
the  plane  belongs  to  a  Dihexagonal  Prism  or  to  one  of 
its  partial  forms : 

a.  If  the  number  of  similar  planes  is  twelve,  then 
each  plane  belongs  to  a  Dihexagonal  Prism. 

b.  If  the  number  of  similar  planes  is  six,  each  plane 
belongs  to  a  Tertiary  Hexagonal  Prism  or  Hexagonal 
Prism  of  the  Third  Order,  provided  its  lateral  angles 
are  equal ;   but  if  the  lateral  angles  are  alternately 
unequal,*  then  each   plane  belongs  to  a   Ditrigonal 
Prism. 

*  In  this  case  three  of  the  alternate  angles  are  equal  to  one  another, 
while  the  three  other  alternate  angles  are  unequal  to  the  first  three,  but 
they  are  all  equal  to  one  another. 


106  NOTES    ON    CRYSTALLOGRAPHY. 

c.  If  the  number  of  similar  planes  is  three,  then  each 
plane  belongs  to  a  Tertiary  Trigonal  Prism  or  Trigonal 
Prism  of  the  Third  Order. 

V.  If  a  plane  intersects  the  vertical  axis,  is  parallel 
to  one  lateral  axis,  and  cuts  the  other  two  lateral  axes 
at,  equal  distances,  it  belongs  to  a  Primary  Pyramid  or 
to  some  one  of  its  partial  forms  : 

a.  If  the  number  of  similar  planes  at  each  end  is  six, 
then   each   plane   belongs  to   a  Primary  Hexagonal 
Pyramid  or  Hexagonal  Pyramid  of  the  First  Order. 

b.  When  the  number  of  similar  planes  at  each  end 
is  three,  and  the  figure  is  placed  with  the  vertical  axis 
perpendicular,  if  the  faces  are  rhombohedral  and  the 
lateral  edges  inclined  to  the  horizon,  then  each  plane 
belongs  to  a  Rhombohedron,  but  if  the  faces  are  trian- 
gular and  the  lateral  edges  horizontal,  then  each  plane 
belongs  to  a  Primary  Trigonal  Pyramid  or  Trigonal 
Pyramid  of  the  First  Order. 

VI.  If  a  plane  cuts  the  vertical  axis  and  intersects 
one  lateral  axis  at  a  unit  of  distance,  cutting  the  other 
two  at  twice  that  distance,  it  is  a  plane  belonging  to  a 
Secondary  Pyramid  or  to  some  of  its  partial  forms  : 

a.  If  the  number  of  similar  planes  at  each  end  is  six, 
then  each  plane  belongs  to  a  Secondary  Hexagonal 
Pyramid  or  Hexagonal  Pyramid  of  the  Second  Order. 

b.  When  the  number  of  similar  planes  at  each  end 
is  three,  and  the  figure  is  placed  with  the  vertical  axis 


THE    HEXAGONAL    SYSTEM.  107 

perpendicular,  if  the  faces  are  rhombohedral  and  the 
lateral  edges  inclined  to  the  horizon,  then  each  plane 
belongs  to  a  Secondary  Rhombohedron,  but  if  the  faces 
are  triangular  and  the  lateral  edges  horizontal,  then 
each  plane  belongs  to  a  Secondary  Trigonal  Pyramid 
or  Trigonal  Pyramid  of  the  Second  Order. 

VII.  If  a  plane  cuts  the  vertical  axis  and  intersects 
all  the  lateral  axes  at  unequal  distances,  the  plane  be- 
longs to  a  Dihexagonal  Pyramid  or  to  some  one  of  its 
partial  forms  : 

a.  If  the  number  of  similar  planes  at  each  end  of  the 
crystal  is  twelve,  then  each  plane  belongs  to  a  Dihexag- 
onal Pyramid. 

b.  If  the  number  of  similar  planes  at  each  end  of 
the  crystal  is  six,  then  each  plane  belongs  to  one  of  the 
four  following  hemihedral  or   half  forms :   (1)  If  the 
alternate  terminal  angles  are  unequal  (three  and  three) 
and  the  lateral  edges  are  zigzag  and  equal,  then  each 
plane  belongs  to  a  Scalenohedron ;  (2)  if  the  terminal 
angles  are  all  equal  and  the  edges  horizontal,  then 
each  plane  belongs  to  the  Tertiary  Hexagonal  Pyramid; 
(3)  if  the  terminal  angles  are  equal  and  the  lateral 
edges  zigzag  and  unequal,  each  plane  belongs  to  a 
Hexagonal  Trapezohedron  ;  (4)  if  the  alternate  termi- 
nal angles  are  unequal  (three  and  three)  and  the  lateral 
edges  horizontal,  each  plane  belongs  to  the  Ditrigonal 
Pyramid. 


108  NOTES    ON    CRYSTALLOGRAPHY. 

c.  If  the  number  of  similar  planes  at  each  end  of  the 
crystal  is  three,  then  each  plane  may  belong  to  one  of 
the  three  following  tetartohedral  or  quarter  forms :  (1) 
If  the  faces  are  rhombohedral  and  the  edges  oblique  to 
the  horizontal  plane,  each  face  belongs  to  a  Tertiary 
Rhombohedron  or  Rhombohedron  of  the  Third  Order ; 
(2)  if  the  faces  are  trapeziums  with  unequal  lateral 
zigzag  edges,  each  face  belongs  to  a  Trigonal  Trapezo- 
hedron ;  (3)  if  the  terminal  angles  are  all  equal,  and 
if  the  faces,  triangles,  and  the  lateral  edges  are  hori- 
zontal, then  each  face  belongs  to  the  Tertiary  Trigonal 
Pyramid  or  Trigonal  Pyramid  of  the  Third  Order.* 

VIII.  If  the  opposite  ends  of  the  crystal  are  unlike, 
the  forms  are  Hemimorphic 

a.  If  the  form  is  composed  of  a  hemi-dihexagonal 
pyramid  and  a  basal  plane,  or  of  hemi-dihexagonal 
and  primary  or  secondary  pyramids  and  prisms  with 
a  basal  plane,  then  the  form  belongs  to  the  lodyrite 
Type. 

*  The  statements  that  the  lateral  edges  are  oblique  or  horizontal,  and 
that  the  planes  are  triangles,  etc.,  refer  to  a  complete  single  form.  In 
the  case  of  compound  forms  the  various  planes  so  modify  one  another 
that  the  positions  of  the  lateral  edges  and  the  shapes  of  the  planes  are 
much  varied.  In  such  cases  the  student  will  need  to  refer  to  the  text 
for  the  relative  positions  of  the  planes  in  each  case,  or  to  reconstruct 
the  complete  form  for  each  set  of  similar  planes  when  handling  com- 
plicated compound  forms,  until  he  has  had  sufficiently  extended  prac- 
tice in  this  work  to  enable  him  to  recognize  readily  the  forms  from  the 
positions  of  their  planes. 


THE    HEXAGONAL    SYSTEM.  109 

b.  If  the  form  is  composed  of  hexagonal  pyramids 
and  prisms  with  or  without  one  or  two  basal  planes, 
then  the  form  belongs  to  the  Nephelite  Type. 

c.  If  the  form  consists  of  a  hemi-hexagonal  or  ditri- 
gonal  pyramid  terminated  by  a  basal  plane,   or  of 
hexagonal    prisms    terminated     by    hemi-hexagonal 
pyramids  and  by  basal  planes,  or  of  hexagonal,  ditri- 
gonal,  and  trigonal  prisms  terminated  by  hemi-rhorn- 
bohedrons,  and  with  or  without  hemi-hexagonal  pyra- 
mids, the  form  belongs  to  the  Tourmaline  Type. 

d.  If  the  form  consists  of  a  hemi-trigonal  pyramid 
or   pyramids  with  or  without  trigonal   prisms,  and 
terminated  on  the  base  by  a  pinacoid,  the  form  belongs 
to  the  Sodium-Periodate  Type.* 

READING    DRAWINGS   OF   HEXAGONAL   CRYSTALS. 

The  four  axes  of  the  Hexagonal  system  render  the 
crystallographic  shorthand  in  that  system  more  com- 
plicated than  in  the  preceding  systems. 

The  lettering  of  the  semi-axes  is  shown  in  Fig.  6 
and  noted  on  page  75.  In  the  preceding  systems  the 
front  semi-axis  and  the  right  semi-axis  are  considered 
as  positive,  while  those  semi-axes  extending  to  the  rear 

*  To  distinguish  between  these  hemimorphic  types  is  not  easy,  and 
the  rules  above  given  are  far  from  accurate,  especially  in  the  case  of  the 
first  three  types.  Frequent  reference  will  have  to  be  made  to  the  text ; 
to  the  centres,  axes  and  planes  of  symmetry  ;  to  the  positions  of  the 
crystallographic  axes,  and  to  the  figures  given  in  the  plates. 


110  NOTES    ON    CRYSTALLOGRAPHY. 

and  to  the  left  are  considered  negative.  Further,  the 
parameter  or  index  of  the  semi-axis  extending  forwards 
or  backwards  is  read  first,  and  that  belonging  to  the 
semi-axis  extending  to  the  right  or  left,  as  the  case 
may  be,  is  read  secondly.  In  the  Hexagonal  system 
the  method  of  reading  the  lateral  semi-axes  is  changed. 
Commencing  with  the  semi-axis  in  front  and  consider- 
ing that  as  positive,  we  call  the  next  semi-axis  to  the 
right  negative.  Continuing  to  read  the  parameters  or 
indices  of  the  lateral  semi-axes  from  the  right  around 
to  the  rear  and  to  the  left  of  the  vertical  axis,  we  desig- 
nate the  third  lateral  semi-axis  as  positive,  the  fourth 
negative,  the  fifth  positive,  and  the  sixth  negative;  or 
the  signs  of  the  axes  alternate  as  we  read  around  the 
vertical  axis  either  from  right  to  left  or  left  to  right. 

In  reading  the  parameters  or  indices,  it  is  the  ap- 
proved modern  method  to  read  first  the  parameter 
belonging  to  the  lateral  semi-axis  in  the  front  or  in 
the  rear ;  secondly,  that  of  the  third  lateral  semi-axis 
to  the  right  or  the  left,  and  thirdly,  that  of  the  second 
lateral  semi-axis.  As  in  the  other  systems,  the  vertical 
semi-axis  is  given  last,  and  is  called  positive  when 
above  the  lateral  axes  and  negative  when  below  them. 

It  should  be  observed,  then,  that  at  least  one  of  the 
lateral  parameters  or  indices  of  any  plane  or  form  in 
the  Hexagonal  system  is  always  negative  (see  page  75), 
while  some  of  the  others  may  be.  In  the  Miller- 


THE    HEXAGONAL    SYSTEM.  Ill 

Bravais  notation  the  majority  of  crystallographers  use 
i  for  the  second  lateral  semi-axis,  i.  e.,  for  the  axis  that 
lies  to  the  right  of  the  lateral  semi-axis  in  the  front. 
It  should  further  be  observed  that  in  this  notation  the 
amount  of  the  lateral  negative  integer  or  integers  is 
exactly  equal  to  the  amount  of  the  lateral  positive  in- 
teger or  integers. 

As  before,  the  hemihedral  forms  are  distinguished, 
in  the  Weiss  notation,  by  writing  J  before  the  symbols 
of  the  form  or  plane,  or,  in  the  Naumann  notation,  by 
writing  2  as  the  denominator  of  a  fraction,  whose 
numerator  is  the  symbol  of  the  corresponding  holohe- 
dral  form. 

In  the  same  way  the  tetartohedral  planes  and 
forms  are  designated  by  writing  J  before  the  Weiss 
symbol,  or,  in  the  Naumann  notation,  by  using  4  as 
the  denominator  and  the  symbol  of  the  holohedral 
form  as  the  numerator  in  each  case. 

In  the  Miller-Bravais  notation  the  hemihedral  planes 
and  forms  are  indicated  by  some  Greek  letter  written 
before  the  indices,  while  those  which  are  tetartohedral 
are  designated  by  any  two  Greek  letters  placed  before 
the  symbols.  Further,  when  the  hemihedral,  or 
selected  tetartohedral  forms  can  be  easily  known  as 
such  by  the  context  or  by  the  figure,  the  Greek  letters 
are  often  omitted  before  the  symbols. 

Most  of  these  symbols  are  quite  easily  understood 


112  NOTES    ON    CRYSTALLOGRAPHY. 

when  they  are  compared  with  those  of  preceding 
systems  as  shown  in  the  various  tables. 

The  symbols  or  crystallographic  shorthand  employed 
in  the  cases  of  the  rhombohedrons  and  scalenohedrons 
in  the  Naumann  system  require  special  mention.  Ac- 
cording to  the  method  of  derivation  of  the  funda- 
mental primary  rhombohedron  (see  page  85),  its  sym- 

p 

bol  in  the  usual  form  would  be-,  but  in  the  Naumann 

system  this  is  usually  abbreviated  as  R.  In  the  cases 
of  the  subordinate  primary  rhombohedrons  the  usual 

symbol  would  be  — ,  but  this  is  abbreviated    as   mR, 

in  which  the  m  may  be  J,  &,  f,  f ,  1,  7,  i,  3,  4,  •§-,  6,  7, 
and  so  on. 

The  more  obvious  symbols  for  the  scalenohedrons 

are    — -    for    the   principal    forms,  and   ^?— —  for  the 

subordinate  forms,  but  these  are  commonly  written  as 
Rn  and  mRn  in  the  Naumann  system.  Dana  further 
abbreviates  these  as  mn. 

Since  the  rhombohedrons  and  scalenohedrons  are 
much  more  common  than  are  the  holohedral  forms,  it 
is  a  matter  of  convenience  to  dispense  with  the  frac- 
tional symbols  in  the  former. 

In  the  hemimorphic  forms,  since  the  opposite  ends 
of  the  crystals  are  unlike,  the  letter  o  is  employed  to 


THE   HEXAGONAL   SYSTEM.  113 

designate  the  forms  that  are  over  or  upon  the  upper 
portion  of  the  crystals,  and  the  letter  u  is  used  to  indi- 
cate those  on  the  under  or  lower  part  of  the  crystal. 
The  employment  of  the  initial  o  for  over  and  u  for 
under  conduces  not  only  to  convenience  in  the  use  of 
other  texts  but  also  to  uniformity,  since  the  German 
crystallographers  employ  the  same  letters :  o  for  ober 
and  u  for  unter. 

In  the  same  way,  crystallographers  use  r  for  right 
(rechts)  or  right-handed  and    I  for  left  (links)  or  left- 
handed  in  connection  with  the  symbols  of  right-handed 
or  left-handed  forms. 
8 


114 


NOTES   ON   CRYSTALLOGRAPHY. 


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116 


NOTES   ON    CRYSTALLOGRAPHY. 


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THE    HEXAGONAL   SYSTEM. 


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THE    HEXAGONAL   SYSTEM.  121 

DIRECTIONS    FOR   STUDYING    HEXAGONAL    CRYSTALS 

1.  Prove  that  the  crystal  or  model  is  hexagonal. 

2.  Locate  the  axes  so  as  to  make  the  forms  as  few 
and  simple  as  possible,  and  place  the  crystal  with  the 
vertical  axis  erect. 

3.  Determine  whether  the  vertical  axis  is  coincident 
with  an  axis   of  hexagonal   or   trigonal   symmetry. 
This  will  separate  the  forms  into  two  divisions :  the 
Hexagonal  and  the  Rhombohedral  or  Trigonal. 

a.  The   Hexagonal   Division  comprises  the   Holo- 
hedral  Forms,  the  Pyramidal  Group,  the  Hexagonal 
Trapezohedrons,    and    the    lodyrite    and    Nephelite 
Types. 

b.  The  Trigonal  Division  comprises  the  Rhombo- 
hedral Group,  the  Ditrigonal  Pyramids,  the  Tetarto- 
hedral    Forms,    and    the   Tourmaline   and    Sodium- 
Periodate  Types. 

4.  Note  the  dominant  and  modifying  forms  in  the 
order  of  their  importance. 

5.  Select  and  name  the  planes  belonging  to  each 
form. 

6.  Distinguish  the  holohedral,  hernihedral,  tetarto- 
hedral  and  hemimorphic  forms,  giving  to  each  its 
appropriate  name. 

7.  Locate  the  planes,  the  remaining  axes,  and  the 
centers  of  symmetry. 


CHAPTER  VII 

ISOMETRIC    SYSTEM 

THIS  system  derives  its  name  from  the  Greek  Isos, 
"  equally  distributed,"  and  Metron,  "  measure  or  pro- 
portion," because  along  its  axes  its  measurements  are 
equal  and  the  holohedral  forms  are  equally  propor- 
tioned. In  this  s}Tstem,  then,  the  three  axes  are  of 
equal  length  and  the  angles  are  all  right  angles,  con- 
sequently there  can  be  no  dominant  unequal  direction 
or  directions.  See  Fig.  5. 

NOMENCLATURE 

Since  the  axes  are  all  equal,  the  semi-axes  can  each 
be  represented  by  a;  and  since  any  one  of  them  can 
be  selected  as  a  vertical  semi-axis  and  the  others  as 
lateral  semi-axes,  the  a  is  in  many  cases  omitted,  the 
parameters  only  being  written. 

As  in  the  other  systems  having  three  axes,  a  plane 
may  intersect  one,  or  two,  or  three  axes ;  and  to  locate 
the  axes  in  any  Isometric  form  they  must  be  so  placed 
that  their  directions  will  form  right  angles  with  one 
another  and  that  their  lengths  will  be  equal. 

The  nomenclature  in  this  system  is  somewhat  ex- 
(122) 


THE    ISOMETRIC    SYSTEM.  123 

tensive  and  complicated,  although  not  so  difficult  as 
is  that  of  the  Hexagonal  System. 

DISTINGUISHING    CHARACTERISTICS    OF    THE    ISOMETRIC 
CRYSTALS 

The  Isometric  crystals  are  distinguished  by  the 
possession  of  three  equal  dimensions  at  right  angles  to 
one  another,  and  by  the  further  fact  that  these  direc- 
tions are  always,  not  only  crystallographic  axes,  but 
also  axes  of  symmetry.  These  axes  of  symmetry  are 
either  tetragonal  or  binary.  In  the  Holohedral  forms 
and  in  the  Pentagonal  Icosi tetrahedrons  the  crystal- 
lographic axes  are  axes  of  tetragonal  symmetry;  but 
in  the  Hemihedral  and  Tetartohedral  forms  the  crys- 
tallographic axes  are  axes  of  binary  symmetry.  This 
equality  of  dimensions  gives  to  all  the  Isometric 
forms,  especially  the  holohedral  ones,  an  appearance 
of  having  been  inscribed  in  a  sphere.  See  Figs.  12, 
15,  17,  52,  53,  56-58  and  328-445. 

FORMS   OF   THE    ISOMETRIC   SYSTEM 

I.  Holohedral  Forms: 

1.  Hexahedron  or  Cube. 

2.  Dodecahedron  or  Rhombic   Dodecahe- 

dron. 

3.  Tetrakis  Hexahedron  or  Tetrahexahe- 

dron. 

4.  Octahedron. 


124  NOTES   ON   CRYSTALLOGRAPHY. 

5.  Trigonal  Triakis  Octahedron,  or  Triakis 

Octahedron,  or  Pyramid  Octahedron, 
or  Trisoctahedron. 

6.  Tetragonal     Triakis     Octahedron,     or 

Icositetrahedron,  or  Trapezohedron. 

7.  Hexakis  Octahedron  or  Hexoctahedron. 

II.  Hemihedral  Forms : 

A.  Oblique  Hemihedral  Forms : 

1.  Tetrahedron : 

a.  Positive. 

b.  Negative. 

2.  Tetragonal  Triakis  Tetrahedron,  or  Tet- 

ragonal Tristetrahedron,  or  Deltoid 
Dodecahedron,  or  Tristetrahedron : 

a.  Positive. 

b.  Negative. 

3.  Trigonal  Triakis  Tetrahedron,  Triakis 

Tetrahedron,  or  Trigonal  Tristetra- 
hedron, Pyramid  Tetrahedron,  or 
Trigon-Dodecahedron : 

a.  Positive. 

b.  Negative. 

4.  Hexakis   Tetrahedron   or   Hextetrahe- 

dron  : 

a.  Positive. 

b.  Negative. 


THE   ISOMETRIC   SYSTEM.  125 

B.  Parallel  Hemihedral  Forms : 

1.  Pentagonal    Dodecahedron   or   Pyrito- 

hedron : 

a.  Positive. 

b.  Negative. 

2.  Dyakis  Dodecahedron  or  Diploid  : 

a.  Positive. 

b.  Negative. 

C.  Gyroidal  or  Plagihedral  Hemihedral  Forms : 

1.  Pentagonal  Icositetrahedron  or  Gyroid  : 

a.  Rightrhanded. 

b.  Left-handed. 
III.  Tetartohedral  Forms : 

1.  Tetrahedral  Petagonal  Dodecahedron  : 

a.  Positive. 

u.  Right-handed. 
w.  Left-handed. 

b.  Negative. 

x.  Right-handed. 
z.   Left-handed. 

I.    HOLOHEDRAL    FORMS 

Given  three  equal  axes  at  right  angles  to  one  an- 
other, it  is  our  first  task  to  see  how  many  complete 
forms  can  be  produced  by  arranging  all  the  planes  we 
can  in  all  possible  positions  about  these  axes. 

1.  Let  the  plane  intersect  one  axis  and  be  parallel 


126  NOTES   ON   CRYSTALLOGRAPHY. 

to  the  other  two,  so  that  its  symbol  will  be  1  :  oo  :  oo  . 
If  we  take  our  model  of  the  Isometric  axes  (see  Fig.  5) 
and  place  our  glass  plate  or  piece  of  cardboard  upon 
it  so  that  it  will  intersect  one  axis  and  be  parallel  to 
the  other  two,  we  find  that  there  are  just  six  positions 
in  which  the  plane  can  be  so  put  as  to  fulfil  these  re- 
quirements; one  at  each  end  of  the  semi-axes. 

If,  then,  planes  be  placed  in  these  positions  and  be 
so  cut  that  their  edges  will  exactly  join  and  make  a 
complete  form,  we  shall  have  a  figure  of  six  equal 
sides,  which  are  all  at  right  angles  to  one  another,  or 
a  form  that  is  called  a  Hexahedron  (Greek,  Hex  and 
Hedra,  which  are  defined  on  pages  18  and  33).  We 
are  all  familiar  with  this  form  under  its  common 
nickname,  the  Cube.  See  Figs.  328,  336  and  387. 

2.  The  next  possible  variation  is  when  the  planes 
cut  two  axes  equally  and  are  parallel  to  the  third 
axis  ;  its  symbol  is  1  :  1  :  oo.  By  placing  the  trial 
plate  about  the  axes  in  all  the  different  positions  in 
which  it  will  fulfil  the  necessary  requirements,  one 
can  ascertain  that  there  are  just  twelve  different  posi. 
tions  in  which  the  plane  can  be  placed.  These  posi- 
tions are  such  that  the  plane  can  join  the  ends  of  two 
of  the  semi-axes  and  still  be  parallel  to  the  third  axis. 
If  enough  planes  are  placed  in  these  positions  and 
extended  until  they  meet,  a  twelve-sided  figure  or 
Dodecahedron  will  be  produced.  This  is  sometimes 


THE    ISOMETRIC   SYSTEM.  127 

called  the  Rhombic  Dodecahedron,  to  distinguish  it 
from  the  other  Dodecahedrons.  The  name  comes 
from  the  Greek,  Dodeka,  "  twelve,"  and  Hedra,  see 
page  23.  See  Fig.  329. 

3.  The  next  variation  in  the  position  of  our  plane 
will  be  to  have  it  cut  two  of  the  axes  unequally  and 
still  remain  parallel  to  the  third  axis ;  its  symbol  is 
1  :  m  :  oo.     By  placing  our  plate  in  all  the  different 
positions  in  which  it  can  be  located  about  the  Iso- 
metric axes  and  still  fulfil  the  above  requirements,  we 
ascertain  that  there  are  twenty-four  such  positions. 
If  we  put  these  twenty-four  planes  about  the  axes  so 
that  each  face  will  cut  one  axis  at  unity  and  the  next 
at  some  greater  distance,  m,  and  will  be  parallel  to 
the  third  axis,  then  we  find  that  each  Hexahedron  or 
Cube  face  has  been  replaced  by  a  pyramid  formed  by 
four  triangles  (6X4=24). 

From  this  combination  we  obtain  the  name  Tetrakis 
Hexahedron,  which  is  derived  from  the  Greek  Tetrakis, 
"  four  times,"  combined  with  Hexahedron,  the  deriva- 
tion of  which  has  already  been  explained  (see  p.  126). 
The  faces,  then,  are  four  triangles  taken  six  times,  or 
twenty-four  triangles.  See  Fig.  330. 

4.  The  next  most  simple  variation  is  to  place  the 
plane  so  as  to  cut  all  three  axes  equally ;  its  symbol 
is  1 :  1  :  1. 

In  this  case  it  will  be  found  that  there  are  eight 


128  NOTES   ON    CRYSTALLOGRAPHY. 

positions  in  which  the  plane  can  be  located  upon  the 
axes  in  such  a  manner  as  to  fulfil  the  requirements 
above  given.  The  placing  of  eight  planes  so  as  to 
intersect  all  the  axes  equally,  and  their  extension  until 
they  join  and  make  a  complete  form,  will  give  rise  to 
the  figure  known  as  the  Octahedron  or  Regular  Octa- 
hedron, whose  faces  are  composed  of  eight  equilateral 
triangles,  and  whose  name  comes  from  the  Greek, 
Okto,  "  eight,"  and  Hedra,  see  page  23.  See  Figs.  12, 
338,  339. 

5.  The  next  variation  is  to  have  the  plane  cut  two 
axes  equally,  and  the  third  axis  at  some  greater  dis- 
tance, ra.  The  symbol  is  1 :  1  :  m. 

By  arranging  our  plate  in  as  many  positions  as  pos- 
sible about  the  axes,  and  still  making  it  agree  with 
the  above  variation,  we  shall  find  that  for  each  octa- 
hedral face  there  are  three  positions  that  answer,  or 
twenty-four  planes.  If  these  twenty-four  planes  are 
put  in  position  and  extended  until  they  all  meet  to 
form  a  complete  whole,  it  is  found  that  all  the  faces 
are  triangles.  Thus  it  is  seen  that  the  form  is  com- 
posed of  three  triangles  multiplied  by  the  complete 
number  of  octahedral  faces  (8),  or  twenty-four  triangles. 
Hence  the  name  Trigonal  Triakis  Octahedron,  mean- 
ing a  form  whose  faces  are  made  by  eight  times  three 
triangles.  This  is  taken  from  the  Greek  Triakis, 
thrice;  see  also  pages  19,  23,  and  128.  The  name  is 


THE    ISOMETRIC    SYSTEM.  129 

often  abbreviated  as  the  Trisoctahedron ;  again,  the 
form  is  occasionally  denominated  the  Pyramid  Octa- 
hedron, because  each  octahedral  face  is  replaced  by  a 
triangular  pyramid  whose  faces  are  triangles.  See 
Fig.  331. 

6.  The  next  variation  is  to  have  the  plane  cut  one 
axis  at  unity  and  the  other  axes  at  a  greater  distance, 
which  shall  be  equal  for  both  these  axes.  The  symbol 
is  1  :  m  :  m. 

If  we  place  the  plate  upon  the  axes  so  as  to  find 
how  many  different  positions  there  are  in  which  it  can 
be  put  and  still  fulfil  the  above  requirements,  it  will 
be  seen  that  there  are  twenty-four.  If  we  place 
twenty-four  planes  in  these  positions  and  extend  them 
so  that  they  will  meet  and  make  a  complete  figure, 
it  will  be  seen  that  the  complete  figure  is  composed  of 
twenty-four  tetragons ;  i.  e.,  three  tetragons  replacing 
each  octahedral  face.  See  Figs.  332  and  333. 

The  name  Tetragonal  Triakis  Octahedron  is  derived 
from  the  Greek,  see  pages  18,  23  and  128.  Other 
names  given  to  it  are  the  Trapezohedron,  because  each 
face  is  a  trapezium  ;  Leucitohedron  or  Leucitoid,  be- 
cause the  mineral  Leucite  crystallizes  in  this  form ; 
and  Icositetrahedron  from  the  Greek  Eikosi,  "  twenty," 
Tetra  (in  composition)  see  page  18,  and  Hedra,  see 
page  23. 

7.  The  next  and  last  possible  variation  is  when  the 
9 


130  NOTES   ON   CRYSTALLOGRAPHY. 

plane  cuts  all  three  axes  at  unequal  distances;  its 
symbol  is  1  :  m  :  n. 

Placing  the  plate  upon  the  axes  so  that  it  will  cut 
all  three  unequally,  we  find  that  there  are  forty-eight 
positions  in  which  the  above  requirements  will  be 
fulfilled,  or  six  for  every  octahedral  face ;  hence  the 
name  Hexakis  Octahedron,  which  is  often  shortened 
to  Hexoctahedron,  from  the  Greek  Hexakis  "six 
times,"  the  entire  name  signifying  "  six  times  eight 
faces,"  or  the  "  forty-eight-faced  form."  It  is  often 
nicknamed  the  Adamantoid  because  the  Diamond 
(Greek  Adamas,  "  adamant ")  crystallizes  in  this  form. 
See  Figs.  334  and  335. 

The  holohedral  forms  have  nine  planes  of  symmetry. 
Three  of  these  form  right  angles  with  one  another  and 
are  coincident  with  the  planes  of  the  crystallographic 
axes.  The  other  six  planes  of  symmetry  unite  the 
diagonally  opposite  edges  of  the  cube  and,  in  the 
center,  are  coincident  with  one  axis  and  make  angles 
of  45°  with  the  other  two.  Since,  in  the  other  holo- 
hedral forms,  they  of  necessity  occupy  the  same  posi- 
tion that  they  do  in  the  cube,  they  can  be  easily 
located  by  comparing  the  other  forms  with  a  cube. 

There  are  also  three  axes  of  tetragonal  symmetry  that 
coincide  with  the  crystallographic  axes  (cubic  axes) ; 
four  axes  of  trigonal  symmetry  (octahedral  axes)  that 
join  the  diagonally  opposite  corners  of  the  cube ;  and 


THE   ISOMETRIC   SYSTEM.  131 

lastly,  six  axes  of  binary  symmetry  that  join  the  centres 
of  the  diagonally  opposite  edges  of  the  cube  (dodecahe- 
dral  axes).  It  can  be  seen  that  the  axes  of  tetragonal 
symmetry  lie  in  the  chief  planes  of  symmetry,  bisect- 
ing them ;  and  that  the  axes  of  binary  symmetry  lie 
in  the  other  six  planes  of  symmetry,  bisecting  them. 
There  is  also  a  center  of  symmetry. 

As  a  matter  of  convenience,  the  above  axes  of  sym- 
metry are  also  considered  as  crystal lographic  axes  and 
are  used  in  descriptions  and  in  calculations. 

1.  The  three  crystallographic  axes  proper  of  this 
system  are  called  Cubic  because  they  are  perpendicu- 
lar to  the  faces  of  the  cube.     See  a,  a,  Fig.  336. 

2.  The  four  axes  that  join  the  diagonally  opposite 
corners  of  the  cube  are  designated  as  Octahedral  be- 
cause they  are  perpendicular  to  the  faces  of  the  octa- 
hedron.    See  b,  6,  Fig.  336. 

3.  The  six  axes  that  join  the  centers  of  diagonally 
opposite  corners  of  the  cube  are  called  Dodecahedral 
because  they  are  perpendicular  to  the  faces  of  the  do- 
decahedron.    See  c,  c,  Fig.  337. 

II.    HEMIHEDRAL    FORMS. 

A.  Oblique  Hemihedral  Forms  : 

These  forms  are  called  oblique  because  the  faces  are 
not  parallel  to  one  another,  but  are  always  so  arranged 
that  they  form  oblique  angles  with  each  other.  See 
Figs.  338-353. 


132  NOTES   ON    CRYSTALLOGRAPHY. 

1.  The  Tetrahedron  can  be  regarded  as  produced 
by  extending,  until  they  meet,  the  alternate  upper  and 
lower  planes  of  the  octahedron,  and  by  suppressing 
the  other  alternate  planes.     This  operation  causes  the 
apices  of  the  octahedron  to  be  prolonged  into  an  edge, 
and  yields  a  four-faced  wedge-shaped  figure  formed  of 
equilateral  triangles,  and  named  Tetrahedron,  from 
the  two  Greek  words  Tetra  and  Hedra,  which  have 
previously  been  defined  (see  pages  18  and  23).     Its 
symbol  in  the  Weiss  notation  is  J  (1  :'  1  : 1),  the  paren- 
theses   being    used   to    denote   Oblique   Hemihedral 
Forms.     See  Figs.  338  and  339. 

If  the  planes  that  were  considered  suppressed  are 
extended  and  those  formerly  extended  are  suppressed, 
another  form  results,  composed  of  the  other  half  of  the 
octahedron.  Singly,  one  tetrahedron  differs  in  no  way 
from  the  other,  except  in  its  position.  In  combina- 
tion, the  planes  of  one  modify  the  solid  angles  of  the 
other,  and  they  are  distinguished  from  each  other  as 
Positive  and  Negative.  See  Figs.  340  and  341. 

If  the  tetrahedron  is  so  placed  that  one  edge  is  hori- 
zontal and  parallel  to  the  observer,  then  the  form  can 
be  called  Positive.  If  another  tetrahedron  is  so 
placed  that  its  horizontal  edge  is  pointing  towards  the 
observer,  the  form  is  Negative. 

2.  The  Tetragonal  Triakis  Tetrahedron  may   be 
considered  as  formed  by  the  extension  of  the  alternate 


THE    ISOMETRIC    SYSTEM.  133 

upper  and  lower  sets  of  three  triangular  faces,  which 
occupy,  in  the  trigonal  triakis  octahedron,  the  posi- 
tions of  the  alternate  faces  of  the  octahedron,  and  by 
the  suppression  of  the  other  alternate  sets  of  three 
planes.  When  the  faces  thus  extended  are  carried 
out  so  as  to  make  a  complete  form,  it  will  be  found 
that  each  face  is  not  a  triangle,  as  in  its  original  form, 
but  is  now  a  tetragon.  See  Figs.  342-345. 

The  completed  form  is  called  Tetragonal  Triakis 
Tetrahedron,  i.  e.,  four  times  three  tetragonal  faces,  a 
name  derived  from  the  Greek,  see  pages  18,  128,  and 
132.  This  is  often  abbreviated  as  the  Tristetrahedron. 
Its  symbol  is  J  (1:1:  m).  There  are  two  forms  to  be 
produced  by  varying  the  sets  of  faces  that  are  to  be 
extended  or  to  be  suppressed,  or  the  Positive  and 
Negative.  The  tetrahedral  edge,  instead  of  being 
straight,  is  broken  and  formed  by  two  lines.  If  this 
broken  edge  is  placed  parallel  to  the  observer,  the 
form  can  be  called  Positive :  but  if  it  is  directed 
towards  the  observer,  it  is  considered  as  Negative. 
See  Figs.  344  and  845. 

3.  The  Trigonal  Triakis  Tetrahedron  may  be  con- 
sidered as  produced  by  the  extension  of  the  alternate 
upper  and  lower  sets  of  three  tetragons  that  occupy 
the  place  of  the  octohedral  faces  in  the  tetragonal 
triakis  octahedron,  and  by  the  suppression  of  the  other 
alternate  sets.  When  the  extended  faces  are  carried 


134  NOTES    ON   CRYSTALLOGRAPHY. 

out  so  as  to  meet,  the  original  tetragons  become 
triangles,  and  the  figure  is  composed  of  four  times 
three  triangular  faces.  See  Figs.  346-349. 

The  name  Trigonal  Triakis  Tetrahedron  is  derived 
from  the  Greek,  see  pages  19, 128,  and  132.  Its  symbol 
is  J  (1:  m:  m).  As  before,  there  are  two  forms,  Posi- 
tive and  Negative.  The  tetrahedral  edge  in  this 
form  is  a  straight  line.  If  this  be  placed  parallel  tos 
the  observer,  then  the  form  can  be  considered  Positive 
but  if  this  edge  is  directed  towards  the  observer,  the 
form  is  Negative.  See  Figs.  348,  349.  The  name  is 
often  abbreviated  as  the  Trigonal  Tristetrahedron. 

The  student  should  always  remember  that  the  hemi- 
hedral  form  of  the  Trigonal  Triakis  Octahedron  is  the 
Tetragonal  Triakis  Tetrahedron,  and  that  of  the 
Tetragonal  Triakis  Octahedron  is  the  Trigonal  Triakis 
Tetrahedron.  See  Figs.  344  and  348. 

4.  The  Hexakis  Tetrahedron,  or,  as  abbreviated,  the 
Hextetrahedron,  can  be  considered  to  be  derived  from 
the  extension  of  the  upper  and  lower  alternate  sets  of 
six  triangles  that  occupy  the  position  of  the  octahedral 
faces  in  the  hexakis  octahedron,  and  by  the  suppression 
of  the  other  sets  of  alternate  faces.  See  Figs.  350  and 
351.  This  procedure  leads  to  the  production  of  six 
triangles  in  the  position  of  each  tetrahedral  face,  or 
four  times  six,  a  fact  which  gives  to  the  form  its  name 
Hexakis  Tetrahedron  (from  the  Greek,  see  pages  130 


THE    ISOMETRIC    SYSTEM.  135 

and  132).  This  form  may  be  either  Positive  or  Nega- 
tive. Its  tetrahedral  edge  is  formed  by  two  broken 
lines.  If  the  form  is  so  placed  that  its  upper  tetra- 
hedral edge  runs  parallel  to  the  observer,  the  form  is 
Positive  ;  but  if  this  edge  is  directed  towards  the  ob- 
server, it  is  Negative.  Its  symbol  is  J(l  :  m  :  ri).  See 
Figs.  352  and  353. 

The  Oblique  Hemihedral  forms  have  six  planes  of 
symmetry  which  lie  parallel  to  the  faces  of  the  dodeca- 
hedron ;  i.  e.,  each  one  lies  parallel  to  one  tetrahedral 
edge,  and  is  perpendicular  to  and  bisects  the  opposite 
tetrahedral  edge. 

These  forms  have  four  axes  of  trigonal  symmetry  that 
extend  perpendicularly  from  each  solid  tetrahedral 
angle  to  the  opposite  tetrahedral  face  in  the  tetra- 
hedron (octahedral  axes) ;  and  which  of  course  occupy 
the  same  positions  in  the  other  oblique  hemihedral 
forms.  They  also  have  three  axes  of  binary  sym- 
metry coincident  with  the  crystallographic  axes,  but 
have  no  center  of  symmetry. 

B.  Parallel  Hemihedral  Forms. 

These  forms  are  called  parallel,  because  every  plane 
has  an  opposite  plane  that  is  parallel  to  it.  See  Figs. 
52,  53,  136,  137  and  356-359. 

The  Pentagonal  Dodecahedron  may  be  considered 
to  be  formed  from  the  tetrakis  hexahedron  by  the  ex- 


136  NOTES    ON    CRYSTALLOGRAPHY. 

tension  of  one  pair  of  planes  touching  at  their  apices, 
in  each  set  of  four  triangles  which  replace  the  faces  of 
the  hexahedron,  and  by  the  suppression  of  the  other 
pair.  If  we  do  this  for  each  replaced  hexahedral 
face,  taking  care  to  alternate  the  pairs  so  that  no  two 
extended  or  two  suppressed  planes  join  base  to  base, 
a  twelve-faced  figure  results,  whose  face  is  a  pentagon 
or  has  five  sides ;  four  of  these  are  equal,  while  the 
fifth  is  bisected  by  the  termination  of  a  crystallo- 
graphic  axis,  and  is  of  unequal  length  as  compared 
with  the  other  four  sides.  See  Figs.  354-359. 

As  the  form  is  composed  of  twelve  pentagons,  it  is 
called  the  Pentagonal  Dodecahedron  (from  the  Greek, 
pente,  "five,"  compounded  with  other  Greek  words 
that  have  been  defined  on  pages  18  and  127).  It  is 
also  commonly  nicknamed  Pyritohedron,  which  may 
be  freely  translated  as  the  Pyrite-faced-figure,  because 
the  mineral  Pyrite  often  crystallizes  in  this  form. 

The  symbol  is  J[l  :  m  :  oo  ];  the  brackets  are  used 
to  distinguish  parallel-faced  forms  in  the  Weiss  system. 

By  extending  the  planes  previously  suppressed,  and 
by  suppressing  those  previously  extended,  another 
Pentagonal  Dodecahedron  results,  which  in  no  way 
differs  from  the  preceding,  except  in  the  position  of  its 
axes.  The  first  is  known  as  Positive  and  the  second 
as  Negative.  If  the  forms  are  so  placed  that  one 
crystallographic  axis  is  perpendicular,  and  if  the  edge 


THE    ISOMETRIC    SYSTEM.  137 

bisected  by  that  axis  is  parallel  to  the  observer,  the 
form  in  question  is  Positive ;  but  if  it  is  directed  to- 
wards the  observer,  then  it  is  Negative.  Again  if  the 
axis  is  horizontal  and  directed  towards  the  observer, 
and  if  the  edge  nearest  him  is  perpendicular,  the 
crystal  is  positive ;  but  if  that  edge  is  horizontal,  the 
form  is  negative.  See  Figs.  52,  53,  356  and  357. 

2.  The  Dyakis  Dodecahedron  can  be  considered  to 
be  formed  by  extending  each  set  of  two  planes  of  the 
hexakis  octahedron  which  answer  to  each  plane  of  the 
Tetrakis  Hexahedron  that  was  extended  or  suppressed 
to  form  the  Pentagonal  Dodecahedron.  If,  then,  each 
set  of  planes  be  extended  or  suppressed  as  was  done  in 
the  preceding  case,  two  forms  result,  Positive  and 
Negative,  each  made  up  of  twenty-four  faces  that  are 
trapeziums.  See  Figs.  136,  137  and  360-364.  If  a 
Dyakis  Dodecahedron  be  placed  with  an  axis  vertical 
and  if  the  broken  edge  that  answers  to  the  edge  of  the 
Pentagonal  Dodecahedron  runs  parallel  to  the  ob- 
server, then  the  form  is  Positive  ;  but  if  it  extends  to- 
wards the  observer,  then  the  form  is  considered  to  be 
Negative.  See  Figs.  136,  137  and  362-364.  The 
name  Dyakis  Dodecahedron  or  Didodecahedron  is  de- 
rived from  the  Greek,  Dyakis,  or  Dis,  "  twice  or 
double,"  united  with  other  Greek  words  that  have 
been  given  on  pages  23  and  127,  meaning  a  double 
dodecahedron  or  twenty-four-faced  figure.  It  is  often 


138  NOTES    ON    CRYSTALLOGRAPHY. 

nicknamed  the  Diploid  (from  the  Greek  Diplos,  "  two- 
fold or  double"  and  oid,  see  page  11).  Haidenger, 
who  gave  the  form  this  name,  states,  in  substance, 
that  he  does  so  because  of  the  peculiar  arrangement  of 
its  surface  into  three  pairs  of  double  twin  planes 
(3x2x2x2=  24).  Its  symbol  is  £  [1  :  m  :  n\ . 

The  Parallel  Hemihedral  forms  possess  three  planes 
of  symmetry  forming  right  angles  with  one  another, 
and  coinciding  with  the  planes  of  the  crystallographic 
axes.  These  forms  also  have  four  axes  of  trigonal 
symmetry  that  join  the  diagonally  opposite  triedral 
solid  angles  in  the  Dyakis  Dodecahedron  (octahedral 
axes)  and  also  the  triedral  solid  angles  that  occupy 
the  same  position  in  the  Pentagonal  Dodecahedron. 
The  three  crystallographic  axes  (cubic  axes)  are  here 
axes  of  binary  symmetry.  There  is  also  a  center  of 
symmetry. 

C.  Gyroidal  Plagiohedral  or  Hemihedral  Forms. 

1.  The  Pentagonal  Icositetrahedron  may  be  con- 
sidered to  be  formed  by  the  extension  of  the  alternate 
planes  of  the  hexakis  octahedron  until  they  meet  and 
by  the  suppression  of  the  other  set  of  alternate  planes. 
By  reversing  this  process  another  twenty-four-faced 
figure  will  result.  Thus  there  are  two  forms  known 
as  Right-handed  and  Left-handed.  See  Figs.  365- 
367. 


THE    ISOMETRIC    SYSTEM.  139 

These  two  forms  can  be  distinguished  by  placing 
one  axis  perpendicular  to  the  observer  and  one  point- 
ing directly  towards  him.  Let  him  look  at  the  edge 
that  begins  at  the  top  of  the  vertical  axis  and  runs 
most  nearly  parallel  with  the  axis  pointing  towards 
him.  If  that  edge  inclines  towards  the  right  of  the 
axis  the  form  is  Right-handed,  but  if  it  inclines  to  the 
left  of  the  axis  it  is  Left-handed.  In  the  case  of  many 
figures  and  also  in  some  models  the  forms  are  inter- 
changed. 

The  faces  of  these  forms  are  all  similar  irregular 
pentagons,  and  the  forms  are  called  Icositetrahedrons 
(see  page  129).  This  is  also  nicknamed  the  Gyroid 
(from  the  Greek  Gyros,  "  round,  bent,  curved  or 
arched "),  because  the  planes  are  arranged  in  an 
irregular  circular  order  about  the  crystal. 

The  Pentagonal  Icositetrahedrons  have  neither 
planes  nor  center  of  symmetry.  They  do  have  three 
axes  of  tetragonal  symmetry  coincident  with  the  crystal- 
lographic  (cubic)  axes,  four  axes  of  trigonal  symmetry 
coincident  with  the  octahedral  axes,  and  six  axes  of 
binary  symmetry  coincident  with  the  dodecahedral 
axes,  or  they  have  all  the  axial  symmetry  of  the 
holohedral  forms. 


140         NOTES  ON  CRYSTALLOGRAPHY. 
III.  TETARTOHEDRAL  FORMS. 

1.  The  Tetrahedral  Pentagonal  Dodecahedron,  or 
the  Tetartoid,  may  be  considered  to  be  formed  by  the 
extension  of  every  set  of  three  alternate  planes  amongst 
every  set  of  six  that  replaced  the  tetrahedral  faces  in 
the  hexakis  tetrahedron,  and  by  the  suppression  of  the 
other  sets  of  three.  By  doing  this  one  obtains  a 
twelve-faced  figure  of  a  tetrahedral  form  with  three 
irregular  pentagonal  faces  replacing  each  tetrahedral 
face.  By  the  alteration  of  the  extended  and  sup- 
pressed faces,  two  forms,  Right-handed  and  Left- 
handed,  result  from  each  hexakis  tetrahedron.  Since 
there  are  two  hexakis  tetrahedrons,  or  a  positive  and 
a  negative  form,  there  will  be  four  of  these  tetarto- 
hedral  forms : 

a.  Positive: 

u.  Right-handed. 
w.  Left-handed. 

b.  Negative : 

x.  Right-handed. 
2.    Left-handed. 

Let  the  student  place  the  Tetrahedral  Pentagonal 
Dodecahedron  with  the  broken  line  (composed  of  three 
zigzag  lines,  and  corresponding  to  the  edge  of  a  tetra- 
hedron) approximately  horizontal  and  parallel  to  him- 
self. If,  then,  the  upper  right-hand  plane  of  the  three 


THE    ISOMETRIC    SYSTEM.  141 

next  to  him  lie  with  its  longest  direction  nearly  hori- 
zontal, the  crystal  is  Positive ;  but  if  the  same  plane 
has  its  longest  direction  standing  nearly  vertical,  the 
crystal  is  Negative.  See  Figs.  369  and  370. 

The  Tetrahedral  Pentagonal  Dodecahedrons  have 
neither  planes  of  symmetry  nor  any  center  of  symmetry. 
They  have  four  axes  of  trigonal  symmetry  that  join  the 
acute  triedral  solid  angles  with  the  opposite  obtuse 
triedral  solid  angles ;  or,  in  other  words,  they  are 
perpendicular  to  the  faces  of  a  tetrahedron.  The 
crystallographic  (cubic)  axes  are  coincident  with  three 
axes  of  binary  symmetry. 

COMPOUND    FORMS. 

Single  forms  are  common  in  the  Isometric  system, 
but  the  union  of  two  or  more  forms  in  a  single  crystal 
is  the  more  general  rule,  as  it  is  in  the  other  systems, 
and  they  are  associated  as  follows: 

1.  The  Holohedral  Forms  can  all  combine  with  one 
another.     See  Figs.  15,  17,  56-58,  and  371-400. 

2.  The   Oblique  Hemihedral  Forms   can   combine 
with  one  another  and  with  the  Cube,  Dodecahedron, 
and   Tetrakis  Hexahedron,  but  are  never  united  with 
the  Parallel  Hemihedral  Forms.     See  Figs.  401-423. 

3.  The  Parallel  Hemihedral  Forms   can  combine 
with  one  another  and  with  the  Cube,  Dodecahedron, 
Trigonal    Triakis   Octahedron,  and    Tetragonal   Triakis 
Octahedron.     See  Figs.  424-445. 


142  NOTES   ON   CRYSTALLOGRAPHY. 

4.  The  Pentagonal  Icositetrahedrons  or  Gyroids  can 
combine  with  each  other  or  with  the  Cube,  Dodecahe- 
dron, TetmUs  Hexahedron,  Octahedron,  Trigonal  Triakis 
Octahedron,  and  Tetragonal  Triakis  Octahedron. 

5.  The  Tetrahedral  Pentagonal  Dodecahedrons  can 
combine  with  one  another  and  with  the  Cube,  Dode- 
cahedron, Pentagonal  Dodecahedron,  Tetrahedron,  Tetra- 
gonal Triakis  Tetrahedron  and   Trigonal  Triakis  Tetra- 
hedron. 

RULES    FOR   NAMING   JSOMETRIC    PLANES. 

In  this  system  the  distinction  of  the  planes  of  one 
form  from  those  of  another  is  accomplished  most 
easily  by  the  use  of  the  parameters.  If  the  student 
has  located  the  axes  correctly  and  determined  the 
parameters  of  a  plane,  and  if  he  remembers  the  name 
of  the  form  that  has  these  parameters,  he  can  at  once 
designate  the  form  to  which  the  plane  belongs.  He 
need  pay  no  attention  to  the  size  or  shape  of  the 
plane ;  for  its  relation  to  the  axes  and  the  number  of 
similar  planes  making  the  complete  form  are  the  only 
points  with  which  he  is  concerned.  If  he  understands 
the  above  statement,  he  can  name  any  plane  in  this 
system  by  the  following  rules : 

I.  If  the  plane  cuts  one  axis  at  unity  and  is  parallel 
to  the  other  two,  that  is,  if  its  symbol  is  1  :  oo  :  oo, 
the  plane  belongs  to  a  Cube. 


THE    ISOMETRIC    SYSTEM.  143 

II.  If  the  plane  cuts  two  axes  at  unity  and  is  par- 
allel to  the  other  one,  that  is,  if  its  S3rmbol  is  1 : 1  :  <x>, 
the  plane  belongs  to  a  Dodecahedron. 

III.  If  the  plane  intersects  two  of  the  axes  un- 
equally and  is  parallel  to  the  third  axis,  that  is,  if  its 
symbol  is  1  :  m  :  oo,  the  plane  belongs  to  one  of  two 
forms : 

a.  If  the  form  has  the  complete  number  of  planes 
(24),  then  the  plane  belongs  to  a  Tetrakis  Hexahedron. 

b.  If  the  form  has  one-half  the  complete  number  of 
planes  (12),  then  the  plane  belongs  to  a  Pentagonal 
Dodecahedron. 

IV.  If  the  plane  cuts  all  three  axes  at  unity,  that 
is,  if  its  symbol  is  1  :  1  :  1,  it  may  belong  to  one  of 
two  forms : 

a.  If  the  form  has  the  complete  number  of  planes 
(8),  then  the  plane  belongs  to  an  Octahedron. 

b.  If  the  form  has  half  the  complete  number  of 
planes  (4),  then  it  belongs  to  a  Tetrahedron. 

V.  If  the  plane  intersects  two  axes  at  unity  and  the 
third  axis  at  a  greater  distance,  that  is,  if  its  symbol  is 
1  :  1  :  m,  it  belongs  to  one  of  two  forms  : 

a.  If  the  form  has  the  complete  number  of  planes 
(24),  then  the  plane  belongs  to  a  Trigonal  Triakis  Oc- 
tahedron. 

b.  If  the  form  has  one-half  the  complete  number  of 
planes  (12),  then  the  plane  belongs  to  a  Tetragonal 
Triakis  Tetrahedron. 


144  NOTES   ON   CRYSTALLOGRAPHY. 

VI.  If  the  plane  cuts  one  axis  at  unity  and  inter- 
sects the  other  two  axes  at  a  distance  which  is  greater 
than  unity,  but  which  is  equal  for  both  axes,  that  is, 
if  its  symbol  is  1  :  ra  :  m,  the  plane  may  belong  to  one 
of  two  forms  : 

a.  If  the  form  has  the  complete  number  of  planes 
(24),  then  the  plane  belongs  to  a  Tetragonal  Triakis 
Octahedron. 

b.  If  the  form  has  half  the  complete  number  of 
planes  (12),  then  the   plane   belongs  to  a  Trigonal 
Triakis  Tetrahedron. 

VII.  If  the  plane  cuts  all  three  axes  unequally, 
that  is,  if  its  symbol  is  1 :  m  :  n,  the  plane  may  belong 
to  one  of  four  forms  : 

a.  If  the  form  has  the  complete  number  of  faces 
(48),  then  the  plane  belongs  to  a  Hexakis  Octahedron. 

b.  If  the  form  has  half  the  complete  number  of 
planes  (24),  it  may  belong  to  one  of  two  forms  : 

1.  If  the  opposite  planes  form  oblique  angles  with 
each  other,  the  planes  belong  to  a  Pentagonal  Icosi- 
tetrahedron  or  Gyroid. 

2.  If  the  opposite  sides  are  parallel,  the  planes  be- 
long to  a  Dyakis  Dodecahedron  or  Diploid. 

c.  If  the  form  has  one-fourth  the  complete  number 
of  planes  (12),  the   planes  belong  to   a  Tetragonal 
Pentagonal  Dodecahedron. 


THE    ISOMETRIC    SYSTEM.  145 

READING    DRAWINGS    OF    ISOMETRIC    CRYSTALS 

Since  in  this  system  all  the  semi-axes  or  parameters 
are  equal,  a  is  the  symbol  used  to  designate  each 
semi-axis,  and  any  plane  cutting  all  the  axes  equally 
would  have  as  its  symbol  la:  la:  la;  but  there  is 
apparently  no  advantage  in  keeping  the  a,  and  our 
symbol  can  as  well  be  written  1:1:1.  As  a  matter 
of  convenience,  the  a  is  dropped  in  this  text,  but  it  is 
retained  in  most  crystallographies  in  which  the  Weiss 
notation  is  used.  The  a  can  readily  be  supplied  in 
the  notation  if  one  desires  to  employ  the  more  com- 
mon form  of  the  Weiss  symbols. 

The  other  symbols  follow  so  closely  those  which 
have  been  given  in  the  other  systems  that  the  stud,ent 
should  have  no  difficulty  in  understanding  them. 

As  stated  on  pages  37  and  111,  Greek  letters  are 
used  to  designate  the  various  partial  forms  in  the 
Miller  notation.  In  the  following  table,  «  is  used  to 
designate  in  that  notation  the  oblique  Hernihedral 
forms ;  T,  to  indicate  the  Parallel  Hemihedral  forms ; 
y,  to  mark  the  Pentagonal  Icositetrahedrons ;  and  *cny 
to  point  out  the  Tetartohedral  forms. 

While   italic   letters   are  used   in   crystallographic 
symbols  in  most  cases,  in  some  publications,  particu- 
larly in  a  few  recent  text-books,  the  common  type  is 
employed. 
10 


146 


NOTES   ON    CRYSTALLOGRAPHY. 


TABLE  VI 
ISOMETRIC   FORMS  AND  NOTATIONS 


Forms. 

Weiss. 

Naumann. 

Dana. 

Miller. 

Hexahedron 

or  Cube. 

1  :  oo  :  oo 

ooOoo 

t-i  or  a 

100 

Dodeca- 

hedron 

1  :   l:oo 

OnO 

i  or  cZ 

110 

Tetrakis  Hex- 

ahedron. 

1  :  m  :  QO 

oo  Om 

i-m 

hkQ 

Octahedron. 

1:    1:1 

0 

1  or  o 

111 

Trigonal  Tri- 
akis   Octa- 

hedron. 

1:    l:m 

mO 

m 

hhl 

Tetragonal 
Triakis  Oc- 

tahedron. 

1  :  m  :  m 

mOm 

m-ra 

hll 

Hexakis 

Octahedron. 

1  :  :m  :  n 

m  On 

m-7i 

hkl 

0 

Tetrahedrons. 

i(l:    1:1) 

2 
O 

Kl) 

Ki  HI  }• 

—  i(l:    1:1) 

2 

-i(D 

M11U 

raO 

Tetragonal 
Triakis  Tet- 
rahedrons. 

-£;;::! 

IT 
_mO 
2 

Km) 

«-{  /i/iZ  }- 
«  «!  WiZ  }• 

7?i  Om 

Trigonal  Tri- 
akis Tetra- 

i(l :  m  :  ?n) 

mOm 

i(m-n) 

*f**f 

hedrons. 

—HI  :  TO  j  m) 

"T" 

—  i(m-n) 

Hdfi 

mOn 

Hexakis   Tet- 

T( I  :  TO  :  71) 

2 

^(m  71) 

«  ^  /i^z  }• 

rahedrons. 

—1(1  :  m  :  ?0 

mOn 

1  /»*«         \ 

—  ^(m-?0 

«'&*. 

2 

Pentagonal 
Dodecahe- 

«!:«:.) 

Too  0771-1 

J(i-m) 

7T  <{   AfcO   }- 

L     2      J 

drons. 

-i(l:m:co) 

Too  Om~] 
IT"  J 

—  i(i-Wl) 

Tr^khO}- 

THE    ISOMETRIC    SYSTEM. 
TABLE  VI— Concluded 


147 


Forms. 

Weiss. 

Naumann. 

Dana. 

Miller. 

Dyakis 
Dodecahe- 
drons. 

i  1  :  m  :  n 
—  £  1  :  m  :  n 

rr)lOu~| 
L~2~  J 
rmOn~| 
L~2~  J 

^  (m-n) 

HM> 

Pentagonal 
Icositetra- 
hedrons. 

$(}  :  m  :  n)r 

^T" 

**•"* 

rUfcU 
y^Zfc^}- 

i(l  :m:n)r 

mOnr 

K»-»)r 

^wj 

Tetrahedral 
Pentagonal 
Dodecahe- 
drons. 

—  i(l  :m  :n)r 

"4~ 
"~4~ 

K«-«)i 

/CTT^j    lkh\ 

-4(1:  :m:»)l 

"~4~ 

-(im-«)( 

KIT  <!  ^Z  }• 

DIRECTIONS    FOR    STUDYING    ISOMETRIC    CRYSTALS 

1.  Prove  that  the  crystal  is  Isometric  by  finding 
that  it  has  three  equal  directions  at  right  angles  to 
one  another.     These  directions  coincide  with  the  crys- 
tallographic  axes  and  with  the  axes  of  tetragonal  or 
binary  symmetry. 

2.  Note  the  dominant  and  modifying  forms  in  the 
order  of  their  importance. 

3.  Determine  the  parameters  (i.  e.,  the  symbol)  of 
each  set  of  similar  planes,  and  from  the  parameters 
name  the  forms  in  accordance  with  the  rules,  distin- 
guishing the  holohedral,  hemihedral,  and  tetartohe- 
dral  forms. 

4.  Locate   the   planes,   axes,   and  centers   of  sym- 
metry. 


CHAPTER  VIII 

MINERAL    AGGREGATES,  PARALLEL    GROWTHS,    AND 
TWINS 

A.  Minerals  are  either  Crystalline  -or  Amorphous, 
from  the  Greek  a,  "  without,"  and  Morphe,  "  form." 
When  Crystalline  they  show  an  internal  crystalline 
structure,  and  may  or  may  not  possess  a  more  or  less 
perfect  crystal  form. 

When  Amorphous  they  have  neither  a  regular  ex- 
ternal form  nor  any  internal  crystalline  structure. 
The  only  apparent  exception  is  when  percolating 
waters  or  other  agents  remove  the  original  material 
partially  or  entirely  and  replace  it  by  other  materials, 
which  assume  the  form  of  the  mineral  it  has  replaced. 
For  example,  a  crystal  of  pyrite  is  often  replaced  by 
the  amorphous  limonite,  which  keeps  the  outlines  of 
the  original  pyrite  crystal ;  something  like  a  wolf  in 
sheep's  clothing.  Minerals  when  they  masquerade  in 
the  form  belonging  to  other  minerals  are  said  to  be 
Pseudomorphs,  from  the  Greek  Pseudes,  "  false,"  and 
Morphe,  "form." 

(148) 


MINERAL  AGGREGATES.  149 

B.  COMPOUND  MINERALS  OR  CRYSTALS 

It  is  usual  to  find  minerals  grown  together  or 
united  either  regularly  or  according  to  some  law,  or 
else  irregularly  or  without  regard  to  any  apparent 
law. 

I.  A  Mineral  Aggregate  is  formed  by  the  irregular 
union  of  many  minerals.     The  minerals  composing 
the  Aggregate   are   generally  imperfect   crystals,  and 
hence  the  Mineral  Aggregate  can  often  be  justly  styled 
a  Crystalline  Aggregate.     See  Fig.  446. 

II.  When  the  minerals  joined  together  are  so  ar- 
ranged that  similar  parts  are  parallel  they  are  called 
Parallel  Growths  or  Parallel  Groups.    See  Figs.  23- 
27,  447-457.     There  may  be  two  divisions  of  these 
growths :  1.  When  all  the  parts  of  a  crystal  are  par- 
allel to  all  the  similar  parts  of  the  conjoined  crystals. 
2.  When  one  part  of  a  crystal  is  parallel  to  the  sim- 
ilar parts  of  its  attached  crystals. 

III.  When  the  two  parts  of  a  crystal  are  joined  so 
that  by  revolving  one  part  180  degrees  it  will  form 
with  the  other  part  a  simple  crystal,  the  crystal  is 
said  to  be  a  Twin.    That  is  to  say  one  part  occupies  a 
reverse  position  relative  to  the  other  part,  so  that  by 
turning  one  of  the  parts  half  way  around  a  simple 
crystal  will  result.     See  Figs.  463-579. 

In  ordinary  language  the  term  twin  refers  to  two 
only  but  in  Crystallography  it  relates  to  two  or  more 


150  NOTES    ON    CRYSTALLOGRAPHY. 

forms  joined  together  by  crystallographic  planes. 
When  the  twinned  form  is  composed  of  three  individ- 
ual crystals  united,  the  individuals  can  be  spoken  of 
as  twins  or  as  trillings.  See  Figs.  517,  565,  567.  If 
there  are  four  or  five  individuals,  then  the  twins  can 
be  designated  as  fourlings  or  fivelings ;  if  there  are 
eight  individuals,  then  the  twins  can  be  called  eight- 
lings;  and  so  on. 

C.  Mineral  Aggregates,  Parallel  Growths,  and  Twinned 
Crystals  form  Reentrant  Angles.    See  Figs.  458,  461, 
464,  466-468,  470,  476,  477,  479,  481-486,  488,  493- 
495,  498-561,  563-565,  567,  571-573. 

It  often  happens  that  owing  to  the  minuteness  of 
he  Reentrant  Angle,  or  from  other  causes,  this  feature 
is  only  brought  out  by  the  minute  structure  of  the 
crystals  or  by  means  of  polarized  light. 

While  Reentrant  Angles  are  usually  considered  to 
indicate  Aggregates,  Parallel  Growths  or  Twins,  yet  there 
are  some  exceptions ;  therefore  every  case  of  these 
angles  needs  to  be  examined  for  itself,  to  see  whether 
it  falls  under  the  common  rule  or  not.  See  Figs. 
471-474. 

D.  Certain  of  the  Parallel   Growths  and   Twins  are 
often   made  up  partly  or  entirely  of  numerous  thin 
plates   that    are    arranged   parallel    to   one  .another. 
When  the  plates  are  extremely  thin,  the  reentrant 
angles  often  show  as  very  fine  parallel  lines  or  striations 


MINERAL    AGGREGATES.  151 

which  look  as  if  they  had  been  scratcKed  by  a  diamond 
point  or  a  needle,  something  like  a  diffraction  grating. 
See  Figs.  452-457,  459-460,  462.  In  most  cases  they 
can  be  seen  only  when  the  mineral  is  held  at  a  special 
angle  or  examined  under  a  lens. 

When  the  striations  are  considered  to  be  due  to  the 
alternate  formation  of  two  different  crystal  faces  the 
structure  is  called  an  Oscillatory  Combination.  It  is 
usual  to  speak  of  the  forms  produced  by  this  combina- 
tion as  simple  or  single  crystals.  This  Oscillation  is 
illustrated  in  the  pyrite  crystals,  which  show  an 
Oscillatory  Combination  of  the  cube  and  pentagonal 
dodecahedron.  See  Figs.  455,  456. 

When  these  striations  are  considered  to  be  caused 
by  parallel  growths  or  by  repeated  twinning  the  struc- 
ture is  designated  as  Polysynthetic  Growths  or  Poly- 
synthetic  Twinning,  as  the  case  may  be,  from  the  Greek 
Polysynthetos  meaning  "  compounded  of  many  things." 
See  Figs.  459-462. 

E.    TWIN    CRYSTALS 

There  are  two  different  classes  of  twins,  which,  for 
convenience,  are  frequently  distinguished  as  follows  : 
I.  Contact  Twins. 
II.  Penetration  Twins. 

These  classes  are  so  closely  allied  that  their  distinc- 
tion one  from  the  other  is  often  difficult  if  not  impos- 


152  NOTES    ON    CRYSTALLOGRAPHY. 

sible.     Fortunately  their  distinction  is  not  an  import- 
ant matter  except  in  well-marked  cases. 
I.    Contact  Twinning 

The  great  majority  of  twinned  crystals  are  united 
by  some  crystallographic  plane  known  as  the  Compo- 
sition Plane.  Such  compound  crystals  are  called 
Contact  Twins.  The  Composition  Plane  is  often,  but 
not  always,  coincident  with  a  plane  known  as  the 
Twinning  Plane.  This  latter  plane  is  the  plane  that 
will  separate  the  twinning  crystal  into  two  parts,  so 
that  if  one  part  is  revolved  180°  and  again  joined  to 
the  other  part,"  the  union  of  the  two  parts  will  make  a 
complete  and  symmetrical  crystal  form. 

The  axis  about  which  one  part  of  the  crystal  is  to 
revolve  180°  is  known  as  the  Twinning  Axis.  It  is 
perpendicular  to  the  twinning  plane.  For  example,  in 
Figs.  463,  465,  469,  471,  473  and  478,  the  plane  a,  b, 
c,  d,  e,  f,  is  not  only  a  composition  plane,  but  also  a 
twinning  plane  ;  for  not  only  are  the  two  parts  united 
by  it,  but  also  if  one  part  of  Fig.  464  is  revolved  180° 
on  the  other,  the  resulting  form  is  the  simple  and 
complete  octahedron  shown  in  Fig.  463.  The  same 
thing  can  be  observed  in  various  other  forms.  See 
Figs.  466-519. 

As  previously  stated,  twin  forms  are  often  desig- 
nated as  trillings,  fourlings,  fivelings,  etc.,  according  to 
the  number  of  individual  forms.  This  repeated  twin- 
ning takes  place  in  two  ways : 


MINERAL    AGGREGATES.  153 

1.  The   twinning    plane   may    remain   parallel   to 
itself,  in   which  case  we  have  the  earlier  described 
Polysynthetic  Twinning.     See   page   151    and   Figs. 
458-461. 

2.  The  twinning  planes  may  change  their  direc- 
tions, giving  rise  to  groups  that  tend  to  assume  more 
or  less  circular  forms.     These  forms  are  often  called 
Cyclic  Twins,  from  the  Greek  Kyklos,  "a  ring,  a  cir- 
cle, a  round  and  circular  body,  a  wheel,  a  sphere  or  a 
globe."     See  figs.  509-514,  516-519. 

II.  Penetration  Twinning 

If  we  imagine  that  one  crystal  can  penetrate  an- 
other and  leave,  mutually  projecting  from  each,  their 
solid  angles,  we  shall  have  a  form  known  as  a  Pene- 
tration Twin.  In  Figs.  522-530,  illustrating  this 
structure,  it  will  be  noticed  that  the  projecting  solid 
angles  of  one  cube  look  as  if  they  had  been  cemented 
upon  the  sides  of  another  cube.  By  the  exercise  of  a 
little  imagination  we  can  readily  suppose  that  the 
lines  connecting  the  edges  of  the  various  solid  angles 
are  produced  so  as  to  complete  the  cube.  Figs.  520, 
521,  531-556  show  similar  Penetration  Twins  of  vari- 
ous other  forms. 

MIMICRY 

The  term  Mimicry  is  employed  to  designate  the 
condition  whereby  a  crystal  belonging  to  one  system- 


154  NOTES    ON    CRYSTALLOGRAPHY. 

may  simulate  the  appearance  of  a  crystal  belonging 
to  another. 

Good  examples  of  the  progressive  steps  taken  by 
one  form  simulating  that  of  another,  can  be  seen  in 
Figs.  557-580.  In  Figs.  557-559  it  is  shown  that  by 
increasing  the  number  of  twin  crystals  of  one  system 
a  form  roughly  resembling  one  belonging  to  another 
system  is  produced.  In  this  case  twinned  ortho- 
rhombic  crystals  produce  a  seemingly  hexagonal  form. 

This  is  observed  in  Aragonite  as  shown  by  Figs. 
563,  551,  561,  564  and  580,  which  Inark  in  the  order 
named  the  progressive  steps  from  a  simple  ortho- 
rhombic  twin  to  a  nearly  complete  hexagonal  crystal. 
This  is  strikingly  shown  in  Figs.  565  and  566  for 
Cerussite  ;  and  in  Figs.  575-579  for  Witherite.  Figs. 
568  and  569  show  the  completed  Mimicry  of  a  hexa- 
gonal crystal  by  the  orthorhombic  Bromelite.  Figs. 
560  and  562  show  simulating  forms  of  Marcasite,  and 
Fig.  567  one  for  Chrysoberyl. 

Figs.  570-574  show  successive  stages  in  the  twinning 
of  the  monoclinic  Phillipsite  until  it  resembles  an 
isometric  dodecahedron. 

By  Mimicry,  it  can  be  seen  from  the  above  examples, 
that  the  simulation,  as  a  rule,  is  only  approximate,  and 
often  quite  largely  imaginary.  In  all  cases  either  de- 
fects in  the  perfection  of  the  form  mimicked  or  its 
'structure  as  observed  in  polarized  light  will  distinguish 
the  real  form  from  the  imitation. 


CHAPTER  IX 

CLEAVAGE 

THE  Cleavage  of  Minerals  is  their  property  of  split- 
ting indefinitely  parallel  to  certain  crystal  planes.  In 
actual  cleavage  it  is  practically  impossible  to  obtain 
cleavage  plates  so  thin  that  they  could  not  be  split  into 
still  thinner  leaves,  provided  we  had  the  necessary  me- 
chanical means  to  accomplish  this. 

It  is  to  be  noted  that  cleavage  in  minerals  does  not 
run  at  random,  but  is  parallel  to  certain  crystal  faces. 
In  designating  the  Cleavage  it  is  customary  to  use  the 
name- of  the  form  to  whose  faces  the  cleavage  is  parallel. 
Thus,  if  the  mineral  splits  parallel  to  the  faces  of  an 
octahedron,  the  cleavage  is  said  to  be  Octahedral. 
Again  if  the  cleavage  runs  parallel  to  the  plane  of  a 
cube,  a  dodecahedron,  a  pinacoid,  a  prism,  a  pyramid, 
or  a  rhombohedron,  then  the  Cleavage  is  said  to  be 
Cubical,  Dodecahedral,  Pinacoidal,  Prismatic,  Pyra.- 
midal,  or  Rhombohedral,  respectively.  In  the  case  of 
pinacoidal  cleavage  it  is  customary  to  designate  the 
pinacoid  to  which  the  cleavage  is  parallel,  as  brachy- 
or  clino-,  or  macro-,  or  ortho-pinacoidal  or  basal,  ac- 

(155) 


156  NOTES    ON    CRYSTALLOGRAPHY. 

cording  to  the  pinacoid  in  question,  whether  it  is  a 
brachy-,  or  clino-  or  a  macro-,  or  an  ortho-,  or  a  basal 
pinacoid. 

The  faces  to  which  the  cleavage  is  parallel  belong  to 
some  of  the  simple  principal  or  dominant  forms. 
From  this  in  order  to  indicate  the  cleavage,  it  is  cus- 
tomary to  use  the  crystallographic  shorthand  by  stating 
that  it  is  parallel  to  0,  or  111,  when  it  is  octahedral ; 
or  in  every  case  it  is  usual  to  employ  the  symbols  of  the 
crystal  planes  that  are  parallel  to  the  cleavage  planes. 

The  principal  cleavages  in  each  system  are  given 
below. 

TRICLINIC    CLEAVAGE 

In  the  Triclinic  system  the  cleavage  is  chiefly  Pina- 
coidal,  and  less  commonly  Prismatic.  The  usual 
symbols  are  as  follows  : 

1.  Basal  Cleavage,  0  P,  0  or  c,  001. 

2.  Brachypinacoidal  Cleavage,  oo  P  oo,  i-1  or  b,  010. 

3.  Macropinacoidal  Cleavage,  oo  P  oo,  i-l  or  a,  100. 

(  oo  P',  I'  or  m,  110. 

4.  Hemiprismatic  Cleavage  |  ^  p>  ^  ^    -^ 

5.  Hemibrachydomatic  Cleavage  <  !„      .'     w' 

I  fpf  oo,  ]_i/?  oil. 

(  'P  oc>  'l-i',  101. 

6.  Hemimacrodomatic  Cleavage  \    - 

I  /^/    <*>    X1"1/'   101- 

The  two  last  cleavages  are  commonly  grouped  as 
Hemidomatic. 


CLEAVAGE.  157 

MONOCLINIC    CLEAVAGE 

In  the  Monoclinic  System  the  most  common  cleav- 
ages are  Pinacoidal  and  Prismatic.  The  chief  cleav- 
ages and  their  symbols  are  as  follows : 

1.  Basal  Cleavage,  0  P.  0  or  c,  001. 

2.  Clinopinacoidal  Cleavage,  oo  P  oo,  i-i\  or  b,  010. 

3.  Orthopinacoidal  Cleavage,  oo  P  65,  i-l  or  a,  100. 

4.  Prismatic  Cleavage,  oc  P,  I  or  m,  110. 

5.  Clinodomatic  Cleavage,  P  co  ,  1-i,  Oil. 

6    Hemiorthodomatic   Cleavage,  \ 

I  -Poo  ,—1-1,101. 

7.  Hemipyramidal    Cleavage,  •<      ' 

v      i  ,  — 1,   JLJ..L. 
ORTHORHOMBIC    CLEAVAGE 

In  the  Orthorhombic  system  the  most  common 
cleavages  are  Pinacoidal  and  Prismatic. 

The  symbols  and  most  cleavages  in  this  system  are : 

1.  Basal  Cleavage,  OP,  0  or  c,  001. 

2.  Brachypinacoidal  Cleavage,  oo  P  oo  ,  i-1  or  b,  010. 

3.  Macropinacoidal  Cleavage,  oo  P  GO  ,  i-i  or  a,  100. 

4.  Prismatic  Cleavage,  oo  P,  I  or  m,  110. 

5.  Brachydomatic  Cleavage,  Poo  ,  1-T,  Oil. 

6.  Macrodomatic  Cleavage,  Poo,  1-T,  101. 

TETRAGONAL    CLEAVAGE 

In  the  Tetragonal  system  the  common  cleavages 


158  NOTES    ON    CRYSTALLOGRAPHY. 

are  Pinacoidal  and  Prismatic,  with  the  more  rarely 
occurring  Pyramidal.  Their  symbols  are  as  follows  : 

1.  Basal  Cleavage,  OP,  0  or  c,  001. 

2.  Primary  Prismatic  Cleavage,  oo  P,  I  or  m,  110." 

3.  Secondary  Prismatic  Cleavage,  oo  P  oo  ,  i-i  or  a, 
100. 

4.  Primary  Pyramidal  Cleavage,  P,  1,  111. 

5.  Secondary  Pyramidal  Cleavage,  2  Poo ,  2-^,  201. 
The  second  and  third  cleavages  are  usually  united 

under  the  general  name  Prismatic ;  the  fourth  and 
fifth  are  commonly  united  under  the  general  term 
Pyramidal. 

HEXAGONAL    CLEAVAGE 

In  the  Hexagonal  System  the  more  common  cleav- 
ages are  Pinacoidal,  Prismatic,  and  Rhombohedral. 
The  chief  cleavages  with  their  symbols  are  as  follows : 

1.  Basal  Cleavage,  0  P,  0  or  c,  0001. 

2.  Primary  Prismatic  Cleavage,  oo  P,  /or  m,  1010. 

3.  Secondary  Prismatic  Cleavage,  oo  P  2,  i-2  or  a, 
1120. 

4.  Primary  Pyramidal  Cleavage,  P,  1,  1011. 

5.  Secondary  Pyramidal  Cleavage,  P  2,  1-2,  1122. 

6.  Rhombohedral  Cleavage,  R,  1,  * «{  1011  J>  or  1011. 
As  in  the  Tetragonal  System,  the  second  and  third 

cleavages  are  united  under  the  general  term  Prismatic, 
and  the  fourth  and  fifth  cleavages  are  coupled  together 
as  Pyramidal. 


CLEAVAGE.  159 

ISOMETRIC    CLEAVAGE  . 

In  the  Isometric  System  the  cleavages  are  Cubic, 
Dodecahedral,  and  Octahedral.  Their  symbols  are 
as  follows : 

Cubic  Cleavage,  oo  0  oo  ,  i-i  or  a,  100. 

Dodecahedral  Cleavage,  oo  0,  i  or  c£,  110. 

Octahedral  Cleavage,  0,  1  or  o,  111. 

PARTINGS 

In  nature  crystals  are  often  subjected  to  pressure 
that  gives  rise  to  a  platy  structure.  The  plates  thus 
produced  are  usually  taken  for  cleavage  laminae. 
Since  these  Parting  Planes  are  parallel  to  crystal- 
lographic  planes,  the  same  symbols  are  given  to  them 
as  to  those  of  the  cleavage  planes ;  that  is,  the  symbol 
is  that  of  the  crystallographic  plane  to  which  the  Part- 
ing is  parallel. 

Since  the  parting  planes  have  been  produced  by 
pressure  and  the  consequent  slipping  of  the  mineral 
particles  on  one  another,  a  parting  structure  can  be  dis- 
tinguished from  true  cleavage  structure  by  the  fact  that 
the  portion  of  the  mineral  lying  between  two  adjacent 
planes  of  parting  shows  no  tendency  to  split  parallel 
to  those  planes.  In  the  mineral  cleavage  there  is  a 
tendency  on  the  part  of  the  mineral  to  split  indefinitely 
along  planes  parallel  to  the  obvious  cleavage  planes. 

There  is  thus,  on  the  one*  hand,  a  resemblance  be- 


160  NOTES    ON    CRYSTALLOGRAPHY. 

tween  mineral  parting  and  parallel  rock  jointing ;  and, 
on  the  other  hand,  a  similar  resemblance  between 
mineral  cleavage  and  rock  or  slaty  cleavage. 

The  part  between  any  two  cleavage  planes  in  a  rock 
or  mineral  tends  to  split  indefinitely  parallel  to  those 
planes;  but  in  the  case  of  rock  jointing  or  mineral  part- 
ing there  is  no  tendency  for  the  rock  or  mineral  between 
two  adjacent  planes  to  split  parallel  to  those  planes. 

To  a  certain  degree  the  resemblance  extends  to  the 
origin  of  each  ;  as  both  parallel  rock  jointing  and  min- 
eral parting  appear  to  be  largely  due  to  pressure  and 
torsion,  and  are  produced  subsequently  to  the  forma- 
tion of  the  rock  or  mineral.  On  the  other  hand  min- 
eral cleavage  is  probably  due  to  the  molecular  structure 
of  the  crystal  or  to  its  mode  of  chemical  formation, 
and  is  congenital  or  was  produced  in  the  crystal  when 
it  was  formed  ;  while  rock  or  slaty  cleavage  seems  to  be 
caused  in  nature  by  pressure  and  chemical  action 
combined,  and  is  produced  subsequently  to  the  deposi- 
tion of  the  rock. 


CHAPTER  X 

CRYSTALLOGRAPHIC    SYMMETRY 

THE  symmetry  of  the  different  crystal  groups  can 
be  conveniently  represented  by  the  method  employed 
by  Gadolin  *  in  1867.  This  method  projects  the  crys- 
tal as  a  sphere  whose  center  is  the  point  of  intersection 
of  the  crystallographic  axes.  The  positions  of  the 
planes  of  symmetry  are  shown  by  the  circle  and  curved 
lines  drawn  within  the  circle.  If  this  circle  or  these 
lines  are  drawn  as  full  lines,  each  one  indicates  a 
plane  of  symmetry ;  if  they  are  shown  as  dotted  or 
broken  lines,  the  plane  of  symmetry  is  wanting.  See 
Figs.  581-612. 

The  crystallographic  axes  are  indicated  by  straight 
lines  marked  at  the  extremities  by  arrow  feathers.  If 
these  axes  are  drawn  as  continuous  black  lines,  each 
axis  is  an  axis  of  symmetry  ;  if  the  axial  lines  are 
formed  by  dots  or  dashes,  making  a  broken  line,  then 
each  axis. is  not  an  axis  of  symmetry.  See  Figs.  581- 

*  Abhandlung  iiber  die  Herleitung  aller  Krystallographischer  Sys- 
tems mit  ihren  Unterabtheilungen  aus  einem  einzigen  Prinzipe  von 
Axel  Gadolin  (1867),  Leipzig,  1896. 

11  (161) 


162  NOTES    ON    CRYSTALLOGRAPHY. 

612.  An  axis  of  binary  symmetry  is  indicated  by  a 
black  spindle-shaped  figure  (Fig.  587);  one  of  trigonal 
symmetry  by  a  black  triangle  (Fig.  592);  one  of  tetra- 
gonal symmetry  by  a  black  quadrilateral  (Fig.  589), 
and  one  of  hexagonal  symmetry  by  a  blaek  hexagon 
(Fig.  593).  The  center  of  symmetry  is  designated  in 
this  book  by  a  small  circle  inclosing  the  centers  of  the 
figures  and  the  central  symbols  of  the  axes  of  sym- 
metry, if  there  are  any. 

A.    TRICLINIC    SYSTEM 

This  system  has  a  center  of  symmetry,  but  it  has 
neither  plane  nor  axis  of  symmetry.  See  pages  19,  20  ; 
Fig.  581. 

B.    MONOCLINIC    SYSTEM 

I.  The  Holohedral  Forms  have  a  plane  of  symmetry, 
an  cms  of  binary  symmetry,  and  a  center  of  symmetry. 
See  pages  40,  41  ;  Fig.  582. 

II.  The  Clinohedral  or  Hemihedral  Forms  have  a 
plane  of  symmetry  but  they  have  neither  axis  nor  center 
of  symmetry.     See  pages  45,  46  ;  Fig.  583. 

C.    ORTHORHOMBIC    SYSTEM 

I.  The  Holohedral  Forms  have  three  planes  of  sym- 
metry, three  axes  of  binary  symmetry,  and  a  center  of 
symmetry.     See  pages  51,  52  ;  Fig.  584. 

II.  The  Hemihedral  Forms  have  three  axes  of  binary 


CRYSTALLOGRAPHIC    SYMMETRY.  163 

symmetry,  but  they  have  neither  plane  nor  center  of 
symmetry.     See  page  55  ;  Fig.  585. 

III.  The  Hemimorphic  Forms  have  two  planes  of 
symmetry  and  one  axis  of  binary  symmetry,  but  they 
have  no  center  of  symmetry.  See  page  56  ;  Fig.  586. 

D.  TETRAGONAL  SYSTEM 

I.  The  Holohedral  Forms  have  five  planes  of  sym- 
metry, one  axis  of  tetragonal  symmetry,  four  axes  of  binary 
symmetry,  and  a  center  of  symmetry.     See  page  64  ;  Fig. 
587. 

II.  The  three  divisions  of  the  Hemihedral  Forms 
have  different  symmetries,  as  follows : 

1.  The  Sphenoidal  Group  has  two  planes  of  symmetry 
and  three  axes  of  binary  symmetry,  but  it  has  no  center 
of  symmetry.     See  pages  66,  67  ;  Fig.  588. 

2.  The  Pyramidal  Group  has  one  plane  of  symmetry, 
one  axis  of  tetragonal  symmetry,  and  a  center  of  symmetry. 
See  pages  68,  69  ;  Fig.  589. 

3.  The  Trapezohedral  Group  has  one  axis  of  tetra- 
gonal symmetry  and  four  axes  of  binary  symmetry,  but  it 
has  neither  plane  nor  center  of  symmetry.     See  page  69  ; 
Fig.  590. 

E.  HEXAGONAL  SYSTEM 

I.  The  Holohedral  Forms  have  seven  planes  of  sym- 
metry, one  axis  of  hexagonal  symmetry,  six  axes  of  binary 
symmetry,  and  a  center  of  symmetry.  See  pages  84,  85  ; 
Fig.  591. 


164  NOTES    ON    CRYSTALLOGRAPHY. 

II.  The  four  divisions  of  the   Hemihedral  Forms 
differ  in  symmetry,  as  follows  : 

1.  The  Rhombohedral  Group  has  three  planes  of  sym- 
metry, one  axis  of  trigonal  symmetry,  three  axes  of  binary 
symmetry,  and  a  center  of  symmetry.     See  pages  90,  91  ; 
Fig.  592. 

2.  The  Pyramidal  Group  has  one  plane  of  symmetry, 
one  axis  of  hexagonal  symmetry,  and  a  center  of  symmetry. 
See  page  93  ;  Fig.  593. 

3.  The  Trapezohedral  Group  has  one  axis  of  hex- 
agonal symmetry  and  six  axes  of  binary  symmetry,  but  it 
has  neither  plane  nor  center  of  symmetry.     See  page  94  ; 
Fig.  594. 

4.  The  Trigonal  Group  has  four  planes  of  symmetry, 
one  axis  of  trigonal  symmetry,  three  axes  of  binary  sym- 
metry, and  a  center  of  symmetry.     See  page  96  ;  Fig. 
595. 

III.  The  three  divisions  of  the  Tetartohedral  Forms 
possess  symmetry  as  follows : 

1.  The  Rhombohedral  Group  has  an  axis  of  trigonal 
symmetry  and  a  center  of  symmetry,  but  it  has  no  plane 
of  symmetry.     See  page  98  ;  Fig.  596. 

2.  The  Trapezohedral  Group  has  an  axis  of  trigonal 
symmetry  and  three  axes  of  binary  symmetry,  but  it  has 
neither  plane  nor  center  of  symmetry.     See  pages  98- 
100 ;  Fig.  597. 

3.  The  Trigonal  Group  has  one  plane  of  symmetry 


CRYSTALLOGRAPHIC    SYMMETRY.  165 

and  one  axis  of  trigonal  symmetry,  but  it  has  no  center 
of  symmetry.  See  pages  101,  102  ;  Fig.  598. 

IV.  The  four  divisions  of  the  Hemimorphic  Forms 
show  diverse  symmetries,  as  follows  : 

1.  The  lodyrite  Type  has  six  planes  of  symmetry  and 
an  axis  of  hexagonal  symmetry,  but  it  has  no  center  of 
symmetry.  See  pages  102,  103  ;  Fig.  599. 

2-  The  Nephelite  Type  has  an  axis  of  hexagonal  sym- 
metry, but  it  has  neither  plane  nor  center  of  symmetry. 
See  page  103  ;  Fig.  600. 

3.  The  Tourmaline  Type  has  three  planes  of  sym- 
metry and  an  axis  of  trigonal  symmetry,  but  it  has  no 
center  of  symmetry.     See  page  103  ;  Fig.  601. 

4.  The  Sodium  Periodate  Type  has  an  axis  of  tri- 
gonal symmetry,  but  it  has  neither  plane  nor  center  of 
symmetry.     See  pages  103,  104  ;  Fig.  602. 

F.   ISOMETRIC    SYSTEM 

I.  The  Holohedral  Forms  have  nine  planes  of  sym- 
metry, three  axes  of  tetragonal  symmetry,  four  axes  of 
trigonal  symmetry,  six  axes  of  binary  symmetry,  and  a 
center  of  symmetry.     See  pages  125-131 ;  Fig.  603. 

II.  The  three  divisions  of  the  Hemihedral  Forms 
show  symmetry  as  follows : 

1.  The  Oblique  Hemihedral  Forms  have  six  planes 
of  symmetry,  four  axes  of  trigonal  symmetry,  and  three 
axes  of  binary  symmetry,  but  they  have  no  center  of  sym- 
metry. See  pages  131-135  ;  Fig.  604. 


166  NOTES    ON    CRYSTALLOGRAPHY. 

2.  The  Parallel  Hemihedral  Forms  have  three  planes 
of  symmetry,  four  axes  of  trigonal  symmetry,  three  axes  of 
binary  symmetry,  and  a  center  of  symmetry.     See  pages 
135-138 ;  Fig.  605. 

3.  The  Gyroidal  Hemihedral  Forms  have  three  axes 
of  tetragonal  symmetry,  four  axes  of  trigonal  symmetry, 
and  six  axes  of  binary  symmetry,  but  they  have  neither 
plane   nor   center   of  symmetry.     See  pages  138,  139; 
Fig.  606. 

4.  The  Tetartohedral  Forms  have  four  axes  of  tri- 
gonal symmetry,  and  three  axes  of  binary  symmetry,  but 
they  have  neither  plane  nor  center  of  symmetry.     See 
pages  140,  141 ;  Fig.  607. 


CHAPTER  XI 

THE  THIRTY-TWO  CLASSES  OF  CRYSTALS 

As  a  result  of  the  labors  of  Frankenheim,  Hessel, 
Bravais,  Gadolin,  and  others  it  is  possible  within  the 
six  crystallographic  systems  to  arrange  thirty-two 
classes  of  crystals  which  shall  be  distinguished  by  a 
difference  in  their  symmetry.  This  method  is  em- 
ployed largely  in  the  more  recent  works  relating  to 
Crystallography  and  Mineralogy,  particularly  in  Eu- 
rope. Perhaps  no  one  has  done  more  in  recent  times 
to  popularize  this  method  of  studying  Crystallography 
than  has  Groth,  whose  work  will  be  chiefly  followed 
below.  Edward  S.  Dana  has  made  extensive  use  of 
these  classes  in  his  valuable  Text-Book  of  Mineralogy 
(1898),  as  have  also  Penfield,  Kraus,  and  Moses  and 
Parsons  in  their  works.  The  chief  class  or  group 
names  used  in  this  book  and  by  Groth  are  denoted  by 
heavy- faced  type. 

A.    TRI CLINIC  SYSTEM 

(1).  I.  Asymmetric  Class,  Unsymmetrical  Class, 
Asymmetric  Group,  Hemihedral  Class,  Hemipina- 
coidal  Class,  Pedial  Class. 

(167) 


168  NOTES    ON    CRYSTALLOGRAPHY. 

This  crystal  form  is  found  only  amongst  artificial 
crystals,  and  was  therefore  not  given  in  the  preceding 
text.  The  form  consists  of  one  face  only,  and  it  has 
no  plane,  axis  or  center  of  symmetry.  (Fig.  608.)  Each 
form  that  consists  of  a  single  face  is  called  a  Pedion 
(Greek  Pedion,  a  "  plain,  flat  or  field  "). 

The  forms  of  the  Asymmetric  Class  are  given  below. 
In  all  these  classes  seven  forms  are  placed. 

1.  First  Pedion  : 

a.  Positive,  100. 

b.  Negative,  100. 

2.  Second  Pedion : 

a.  Positive,  010. 

b.  Negative,  010. 

3.  Third  Pedion : 

a.  Positive,  001. 

b.  Negative,  001. 

4.  Primary  Pedion,  Qkl. 

5.  Secondary  Pedion,  hOL 

6.  Tertiary  Pedion,  MO. 

7.  Quaternary  Pedion,  hkl 

(2.)  II.  Pinacoidal  Class,  Holohedral  Class,  Centro- 
symmetric  Class,  Normal  Group.  See  pages  19,  20 
and  162  ;  Fig.  581. 

The  forms  of  this  class  are  as  follows  : 

1.  First  Pinacoid,  100. 

2.  Second  Pinacoid,  010. 


THE    THIRTY-TWO    CLASSES    OF    CRYSTALS.          169 

3.  Third  Pinacoid,  001. 

4.  Primary  Pinacoid,  OH. 

5.  Secondary  Pinacoid,  hOL 

6.  Tertiary  Pinacoid,  hkO. 

7.  Quaternary  Pinacoid,  hkl. 

B.    MONOCLINIC    SYSTEM 

(3).  I.  Sphenoidal  Glass,  Hemimorphic  Glass. 

The  forms  of  this  class  have  one  axis  of  binary  sym- 
metry, but  they  have  neither  plane  nor  center  of  sym- 
metry. Fig.  609. 

As  crystals  of  this  class  occur  only  in  artificial  pro- 
ducts like  lithium  sulphate,  sugar,  tartaric  acid,  etc., 
they  have  not  been  mentioned  on  the  preceding  pages. 
The  forms  of  this  class  are  as  follows : 

1.  First  Pinacoid,  100. 

2.  Second  Pedion : 

a.  Right-handed,  010. 

b.  Left-handed,  010. 

3.  Third  Pinacoid,  001. 

4.  Primary  Sphenoid,  Okl. 

5.  Secondary  Pinacoid,  hQL 

6.  Tertiary  Sphenoid,  hkQ. 

7.  Quaternary  Sphenoid,  hkl. 

(4).  II.  Domatic  Class,  Clinohedral  Group,  Hemi- 
hedral  Class.  See  pages  48,  162  ;  Fig.  583. 


170  NOTES    ON    CRYSTALLOGRAPHY. 

The  forms  are  as  follows : 

1.  First  Pedion : 

a.  Positive  [Front],  100. 

b.  Negative  [Back],  100. 

2.  Second  Pinacoid,  010. 

3.  Third  Pedion  : 

a.  Positive  [Over] ,  100. 

b.  Negative  [Under],  TOO. 

4.  Primary  Dome,  Okl. 

5.  Secondary  Pedion,  hQL 

6.  Tertiary  Dome,  hkO. 

7.  Quaternary  Dome,  hkl. 

(5).  III.  Prismatic  Class,  Holohedral  Class,  Normal 
Group.     See  pages  45,  162  ;  Fig.  582. 
Forms : 

1.  First  Pinacoid,  100. 

2.  Second  Pinacoid,  010. 

3.  Third  Pinacoid,  001. 

4.  Primary  Prism,  Qkl 

5.  Secondary  Pinacoid,  hQl. 

6.  Tertiary  Prism,  MO. 

7.  Quaternary  Prism,  hkl. 

C.   ORTHORHOMBIC  SYSTEM 

(6).  I.  Bisphenoidal  Class,  Hemihedral  Class,  Sphe- 
noidal  Group,  Tetrahedral  Hemihedral  Class.  See 
pages  51,  52,  162,  163 ;  Fig.  585. 


THE    THIRTY-TWO    CLASSES    OF    CRYSTALS.          171 

Forms : 

1.  First  Pinacoid,  100. 

2.  Second  Pinacoid,  010. 

3.  Third  Pinacoid,  001. 

4.  Primary  Prism,  Okl. 

5.  Secondary  Prism,  hOL 

6.  Tertiary  Prism,  MO. 

7.  Sphenoid,  hkl. 

(7).  II.  Pyramidal  Class,  Hemimorphic  Class.     See 
pages  56,  163  ;  Fig.  586. 
Forms : 

1.  First  Pinacoid,  100. 

2.  Second  Pinacoid,  010. 

3.  Third  Pedion : 

a.  Over,  001. 

b.  Under,  OOL 

4.  Primary  Dome,  OK. 

5.  Secondary  Dome,  hOL 

6.  Tertiary  Prism,  hkQ. 

7.  Quaternary  Pyramid,  hkl. 

(8).  III.  Bipyramidal  Class,  Holohedral  Class,  Nor- 
mal Group.     See  pages  51,  52,  162  ;  Fig.  584. 

Forms : 
-•>;-.  1.  First  Pinacoid,  100. 

2.  Second  Pinacoid,  010. 

3.  Third  Pinacoid,  001. 

4.  Primary  Prism,  Qkl. 


172  NOTES    ON    CRYSTALLOGRAPHY. 

5.  Secondary  Prism,  hOL 

6.  Tertiary  Prism,  MO. 

7.  Pyramid,  likl. 

D.   TETRAGONAL     SYSTEM 

(9).  I.  Bisphenoidal  Class,  Sphenoidal  Tetartohe- 
dral  Class,  Tetartohedral  Group,  Tetartohedral  Class, 
Tetrahedral  Tetartohedral  Class. 

The  forms  of  this  class  have  one  axis  of  binary  sym- 
metry, but  they  have  neither  plane  nor  center  of  sym- 
metry. See  Fig.  610. 

As  there  is  no  known  example  of  this  class,  the 
forms  have  not  been  mentioned  in  the  earlier  pages  of 
this  book. 

Forms : 

1.  Basal  Pinacoid,  001. 

2.  Primary  Prism,  110. 

3.  Secondary  Prism,  100. 

4.  Tertiary  Prism,  hkQ. 

5.  Primary  Sphenoid,  hhl. 

6.  Secondary  Sphenoid,  hOl. 

7.  Tertiary  Sphenoid,  hkl. 

(10).  II.  Pyramidal  Class,  Hemimorphic  Hemihe- 
dral  Class,  Hemimorphic  Tetartohedral  Class,  Pyra- 
midal Hemimorphic  Class,  Hemimorphic  Group  of  the 
Pyramidal  Hemihedral  Class,  Class  of  Tetragonal 
Pyramid  of  the  Third  Order,  Tetartomorphic  Class. 


THE    THIRTY-TWO    CLASSES    OF    CRYSTALS.          173 

These  forms  have  one  axis  of  tetragonal  symmetry,  but 
they  have  neither  plane  nor  center  of  symmetry.  See 
Fig.  611. 

Inasmuch  as  Wulfenite  is  the  only  mineral  assigned 
to  this  class,  and  there  is  reason  to  doubt  whether  it 
really  belongs  in  this  group,  the  Pyramidal  Class  was 
not  touched  upon  in  the  earlier  pages  of  this  book. 

Forms : 

1.  Basal  Pinacoid  : 

a.  Over  [Positive],  OOJ. 

b.  Under  [Negative] ,  001. 

2.  Primary  Prism,  110. 

3.  Secondary  Prism,  100. 

4.  Tertiary  Prism,  hkO. 

5.  Primary  Pyramid,  hhl. 

6.  Secondary  Pyramid,  hQL 

7.  Tertiary  Pyramid,  hkl. 

(11).  III.  Scalenohedral  Class,  Sphenoidal  Hemi- 
hedral  Class,  Tetrahedral  Hemihedral  Class,  Sphe- 
noidal Group. 

According  to  the  majority  of  crystallographers  this 
class,  in  the  preceding  text,  is  said  to  have  two  planes 
of  symmetry  and  three  .axes  of  binary  symmetry,  but  to 
have  no  center  of  symmetry.  Groth,  and  after  him 
Moses  and  Parsons,  give  the  symmetry  of  this  class  as 
follows  :  Two  planes  of  symmetry,  one  axis  of  tetragonal 
symmetry,  and  two  axes  of  binary  symmetry,  but  no  center 
of  symmetry. 


174  NOTES    ON    CRYSTALLOGRAPHY. 

The  axis  of  tetragonal  symmetry  is  coincident  with 
the  vertical  axis  of  each  form.  See  pages  66,  67,  163 ; 
Fig.  588. 

Forms : 

1.  Basal  Pinacoid,  001. 

2.  Primary  Prism,  110. 

3.  Secondary  Prism,  100. 

4.  Ditetragonal  Prism,  MO. 

5.  Primary  Sphenoid,  hhl. 

6.  Secondary  Pyramid,  hOL 

7.  Scalenohedron,  hkl 

(12).  IV.  Trapezohedral  Class,  Trapezohedral 
Group,  Trapezohedral  Hemihedral  Class.  See  pages 
69,  163  ;  Fig.  590. 

Forms : 

1.  Basal  Pinacoid,  001. 

2.  Primary  Prism,  110. 

3.  Secondary  Prism,  100. 

4.  Ditetragonal  Prism,  MO. 

5.  Primary  Pyramid,  hhl. 

6.  Secondary  Pyramid,  hQl. 

7.  Trapezohedron,  hkl. 

(13).  V.  Bipyramidal  Class,  Pyramidal  Group,  Pyr- 
amidal Hemihedral  Class.  See  pages  68,  69,  163; 
Fig.  589. 

Forms : 

1.  Basal  Pinacoid,  001. 


THE    THIRTY-TWO    CLASSES    OF    CRYSTALS.          175 

2.  Primary  Tetragonal  Prism,  110. 

3.  Secondary  Tetragonal  Prism,  100. 

4.  Tertiary  Tetragonal  Prism,  hkO. 

5.  Primary  Tetragonal  Pyramid,  hhl. 

6.  Secondary  Tetragonal  Pyramid,  hOL 

7.  Tertiary  Tetragonal  Pyramid,  hkl. 

(14).  VI.  Ditetragonal  Pyramidal  Class,  Hemi- 
morphic  Holohedral  Class,  Hemimorphic  Group, 
Pyramidal  Hemihedral  Class,  Class  of  the  Ditetra- 
gonal Pyramid,  Hemimorphic  Hemihedral  Class. 

The  forms  of  this  class  possess  four  planes  of  sym- 
metry and  one  tetragonal  axis  of  symmetry,  but  no  center 
of  symmetry.  As  no  mineral  is  known  to  occur  in  the 
Ditetragonal  Pyramidal  Class,  this  group  was  omitted 
from  the  earlier  part  of  this  work.  See  Fig.  612. 

Forms : 

1.  Basal  Pinacoid  : 

a.  Over  [Positive],  001. 

b.  Under  [Negative],  001. 

2.  Primary  Tetragonal  Prism,  110. 

3.  Secondary  Tetragonal  Prism,  100. 

4.  Ditetragonal  Prism,  hkQ. 

5.  Primary  Tetragonal  Pyramid,  hhl. 

6.  Secondary  Tetragonal  Pyramid,  hOl. 

7.  Ditetragonal  Pyramid,  hkl. 

(15).  VII.  Ditetragonal  Bipyramidal  Class,  Holo- 
hedral Class,  Normal  Group,  Class  of  the  Ditetra- 
gonal Bipyrarnid.  See  pages  64,  163  ;  Fig.  587. 


176  NOTES    ON    CRYSTALLOGRAPHY. 

Forms  : 

1.  Basal  Pinacoid,  001. 

2.  Primary  Tetragonal  Prism,  110. 

3.  Secondary  Tetragonal  Prism,  100. 

4.  Ditetragonal  Prism,  hkQ. 

5.  Primary  Tetragonal  Pyramid,  hhl. 

6.  Secondary  Tetragonal  Pyramid,  hOL 

7.  Ditetragonal  Pyramid,  hkl. 

E.    HEXAGONAL    SYSTEM 

A.   Trigonal  or  Rhombohedral  Division 

(16).  I.  Trigonal  Pyramidal  Class,  Ogdohedral 
Class,  Ogdomorphous  Class,  Hemimorphic  Tetarto- 
hedral  Class,  Hemimorphic  Trigonal  Tetartohedral 
Class,  Sodium  Periodate  Type,  Class  of  the  Hemi- 
morphic Trigonal  Pyramid  of  the  Third  Order.  See 
pages  103,  104,  165  ;  Fig.  602. 

Forms : 

1.  Basal  Pinacoid : 

a.  Over  [Positive],  0001. 

b.  Under  [Negative],  OOOL 

2.  Primary  Trigonal  Prism  : 

a.  Positive,  1010. 

b.  Negative,  1010. 

3.  Secondary  Trigonal  Prism:      ; 

a.  Right-handed,  1120. 

b.  Left-handed,  2110. 


THE   THIRTY-TWO    CLASSES    OF    CRYSTALS.          177 

4.  Tertiary  Trigonal  Prism,  MlO. 

5.  Primary  Trigonal  Pyramid,  hQhl. 

6.  Secondary  Trigonal  Pyramid,  h.h.2h.l. 

7.  Tertiary  Trigonal  Pyramid,  hkll. 

(17).  II.  Rhombohedral  Class,  Rhombohedral  Te- 
tartohedral  Class,  Trigonal  Tetartohedral  Class,  Class 
of  the  Rhombohedron  of  the  Third  Order,  Tri-rhom- 
bohedral  Group,  Trigonal  Rhombohedral  Class.  See 
pages  98,  164  ;  Fig.  596. 

Forms : 

1.  Basal  Pinacoid,  0001. 

2.  Primary  Hexagonal  Prism,  1010. 

3.  Secondary  Hexagonal  Prism,  1120. 

4.  Tertiary  Hexagonal  Prism,  hklQ. 

5.  Primary  Rhombohedron,  hQhl 

6.  Secondary  Rhombohedron,  h.h.2h.l. 

7.  Tertiary  Rhombohedron,  hkil. 

(18).  III.  Trigonal  Trapezohedral  Class,  Trapezo- 
hedral  Tetartohedral  Class,  Class  of  the  Trigonal  Tra- 
pezohedron,  Trapezohedral  Group.  See  pages  98-100, 
164 ;  Fig.  597. 

Forms : 

1.  Basal  Pinacoid,  0001. 

2.  Primary  Hexagonal  Prism,  1010. 

3.  Secondary  Trigonal  Prism,  1120. 

4.  Ditrigonal  Prism,  hklQ. 

5.  Primary  Rhombohedron, 
12 


178  NOTES   ON    CRYSTALLOGRAPHY. 

6.  Secondary  Trigonal  Pyramid,  h.h.Zh.L 

7.  Trigonal  Trapezohedron,  hkil. 

(19).  IV.  Trigonal  Bipyramidal  Class,  Trigonotype 
Tetartohedral  Class,  Sphenoidal  Tetartohedral  Class, 
Trigonal  Tetartohedral  Class,  Trigonal  Group,  Class  of 
the  Trigonal  Bipyramid  of  the  Third  Order,  Class  of 
the  Trigonal  Pyramid  of  the  Third  Order. 

There  is  no  example  of  this  class  known.  See 
pages  101,  164 ;  Fig.  598. 

Forms : 

1.  Basal  Pinacoid,  0001. 

2.  Primary  Trigonal  Prism,  1010. 

3.  Secondary  Trigonal  Prism,  1120. 

4.  Tertiary  Trigonal  Prism,  hklQ. 

5.  Primary  Trigonal  Pyramid,  hOhl 

6.  Secondary  Trigonal  Pyramid,  h.h.2h.l. 

7.  Tertiary  Trigonal  Pyramid,  hkll. 

(20).  V.  Ditrigonal  Pyramidal  Class,  Hemimorphic 
Hemihedral  Class,  Ditrigonal  Pyramidal  Tetartohedral 
Class,  Rhornbohedral  Hemihedral  Class,  Hemimorphic 
Trigonal  Hemihedral  Class,  Class  of  the  Ditrigonal 
Pyramid,  Hemimorphic  Class,  Rhornbohedral  Hemi- 
morphic Class,  Hemimorphic  Rhornbohedral  Hemi- 
hedral Class,  Second  Hemimorphic  Tetartohedral 
Class,  Tourmaline  Type.  See  pages  103,  165 ;  Fig. 
601. 


THE    THIRTY-TWO    CLASSES    OF    CRYSTALS.          179 

Forms : 

1.  Basal  Pinacoid : 

a.  Over,  0001. 

b.  Under,  OOOf. 

2.  Primary  Trigonal  Prism  : 

a.  Positive,  lOlO. 

b.  Negative,  1010. 

3.  Secondary  Hexagonal  Prism,  1120. 

4.  Ditrigonal  Prism,  hkiQ. 

5.  Primary  Trigonal  Pyramid,  htihl. 

6.  Secondary  Hexagonal  Pyramid,  h.h.2h.L 

7.  Ditrigonal  Pyramid,  hkll. 

(21).  VI.  Ditrigonal  Scalenohedral  Class,  Rhombo- 
hedral  Hemihedral  Class,  Scalenohedral  Rhombo- 
hedral  Class,  Class  of  the  Ditrigonal  Scalenohedron, 
Scalenohedral  Class,  Normal  Rhombohedral  Group, 
Rhombohedral  Group.  See  pages  90,  91,  164 ;  Fig. 
592. 

Forms : 

1.  Basal  Pinacoid,  0001. 

2.  Primary  Hexagonal  Prism,  1010. 

3.  Secondary  Hexagonal  Prism,  1120. 

4.  Dihexagonal  Prism,  hk~Q. 

5.  Primary  Rhombohedron,  hfthl. 

6.  Secondary  Hexagonal  Pyramid,  h.h.2h.l. 

7.  Hexagonal  Scalenohedron,  hlcll. 

(22)    VII.  Ditrigonal  Bipyramidal  Class,  Trigono- 


180  NOTES    ON    CRYSTALLOGRAPHY. 

type  Hemihedral  Class,  Sphenoidal-Hemihedral  Class, 
Trigonnl  Hemihedral  Class,  Class  of  the  Ditrigonal 
Bipyramid,  Class  of  the  Ditrigonal  Pyramid,  Trigonal 
Group.  No  examples  are  known  of  this  class.  See 
pages  96,  164 ;  Fig.  595. 
Forms  : 

1.  Basal  Pinacoid,  0001. 

2.  Primary  Trigonal  Prism,  1010. 

3.  Secondary  Hexagonal  Prism,  1120. 

4.  Ditrigonal  Prism,  hklO. 

5.  Primary  Trigonal  Pyramid,  hQhl. 

6.  Secondary  Hexagonal  Pyramid,  h.h.2h.l. 

7.  Ditrigonal  Pyramid,  hkll. 

B.  Hexagonal  Division 

(23).  VIII.  Hexagonal  Pyramidal  Class,  Hemimor- 
phic  Hemihedral  Class,  First  Hemimorphic  Tetarto- 
hedral  Class,  Tetartomorphic  Class,  Hemimorphic 
Pyramidal  Hemihedral  Class,  Pyramidal  Hemimor- 
phic Class,  Hexagonal  Pyramidal  Tetartohedral  Class, 
Class  of  the  Third  Order  Hexagonal  Pyramid,  Nephe- 
lite  Type.  See  pages  103,  165  ;  Fig.  600. 

Forms : 

1.  Basal  Pinacoid : 

a.  Over  [Positive],  0001. 

b.  Under  [Negative],  0001. 

2.  Primary  Hexagonal  Prism,  1010. 


THE    THIRTY-TWO    CLASSES    OF    CRYSTALS.          181 

3.  Secondary  Hexagonal  Prism,  1120. 

4.  Tertiary  Hexagonal  Prism,  hk7Q. 

*5.  Primary  Hexagonal  Pyramid,  hOhl. 

6.  Secondary  Hexagonal  Pyramid,  h.h.2h.L 

7.  Tertiary  Hexagonal  Pyramid,  hkil. 

(24).  IX.  Hexagonal  Trapezohedral  Class,  Trape- 
zohedral Hemihedral  Class,  Trapezohedral  Class, 
Trapezohedral  Group,  Class  of  the  Hexagonal  Trape- 
/ohedron. 

Only  some  artificial  chemical  compounds  occur  in 
the  forms  of  this  class.  See  pages  94,  164  ;  Fig.  594. 

Forms : 

1.  Basal  Pinacoid,  0001. 

2.  Primary  Hexagonal  Prism,  1010. 

3.  Secondary  Hexagonal  Prism,  1120. 

4.  Dihexagonal  Prism,  hklQ. 

5.  Primary  Hexagonal  Pyramid,  hQhl. 

6.  Secondary  Hexagonal  Pyramid,  h.h.2h.l. 

7.  Hexagonal  Trapezohedron,  hlcil. 

(25).  X.  Hexagonal  Bipyramidal  Class,  Pyramidal 
Hemihedral  Class,  Bipyramidal  Class,  Pyramidal 
Group,  Tripyramidal  Group,  Class  of  the  Third  Order 
Hexagonal  Bipyramid,  Class  of  the  Third  Order  Hex- 
agonal Pyramid.  See  pages  93,  164  ;  Fig.  593. 
Forms : 

1.  Basal  Pinacoid,  0001. 

2    Primary  Hexagonal  Prism,  1010. 


182  NOTES    ON    CRYSTALLOGRAPHY. 

3.  Secondary  Hexagonal  Prism,  1120. 

4.  Tertiary  Hexagonal  Prism,  hklQ. 

5.  Primary  Hexagonal  Pyramid,  hOhl. 

6.  Secondary  Hexagonal  Pyramid,  h.h.2h.l. 

7.  Tertiary  Hexagonal  Pyramid,  hkll. 

(26.)  XL  Dihexagonal  Pyramidal  Class,  Hexagonal 
Hemimorphic  Class,  Hemimorphic  Holohedral  Class, 
Hemimorphic  Hemihedral  Class,  Hemimorphic  Group, 
Class  of  the  Dihexagonal  Pyramid,  Class  of  Hemimor- 
phic Dihexagonal  Pyramid,  lodyrite  Type-  See  pages 
102,  165 ;  Fig.  599. 

Forms : 

1.  Basal  Pinacoid  : 

a.  Over  [Positive] ,  0001. 

b.  Under  [Negative] ,  OOOl. 

2.  Primary  Hexagonal  Prism,  1010. 

3.  Secondary  Hexagonal  Prism,  1120. 

4.  Dihexagonal  Prism,  hkiO. 

5.  Primary  Hexagonal  Pyramid,  hQhl 

6.  Secondary  Hexagonal  Pyramid,  h.h.2h.l. 

7.  Dihexagonal  Pyramid,  hkil. 

(27).  XII.  Dihexagonal  Bipyramidal  Class,  Holo- 
hedral Hexagonal  Class,  Holohedral  Class,  Holohedral 
Group,  Normal  Group,  Class  of  Dihexagonal  Pyramid, 
Class  of  the  Dihexagonal  Bipyramid.  See  pages  84, 
85,  163  ;  Fig.  591. 


THE   THIRTY-TWO   CLASSES    OF   CRYSTALS.          183 

Forms : 

1.  Basal  Pinacoid,  0001. 

2.  Primary  Hexagonal  Prism,  1010. 

3.  Secondary  Hexagonal  Prism,  1120. 

4.  Dihexagonal  Prism,  hkW. 

5.  Primary  Hexagonal  Pyramid,  hOhl. 

6.  Secondary  Hexagonal  Pyramid,  h.h.2h.l. 

7.  Dihexagonal  Pyramid,  hkil. 

F.    ISOMETRIC    SYSTEM 

(28).  I.  Tetrahedral  Pentagonal  Dodecahedral 
Class,  Tetartohedral  Class,  Tetartohedral  Gr«up,  Class 
of  the  Tetartoid.  See  pages  140,  166  ;  Fig.  607. 

Forms : 

1.  Hexahedron  or  Cube,  100. 

2.  Dodecahedron,  110. 

3.  Tetrahedron : 

a.  Positive,  111. 

b.  Negative,  111. 

4.  Pentagonal  Dodecahedron  : 

a.  Right-handed,  hkO. 

b.  Left-handed,  khO. 

5.  Trigonal  Triakis  Tetrahedron  : 

a.  Positive,  Jill. 

b.  Negative,  hit. 

6.  Tetragonal  Triakis  Tetrahedron  : 

a.  Positive,  hhl. 

b.  Negative,  hhl. 


184  NOTES    ON    CRYSTALLOGRAPHY. 

7.  Tetrahedral  Pentagonal  Dodecahedron  : 
a    Positive  Right-handed,  hkl. 
b    Positive  Left-handed,  Ikh. 
c.  Negative  Right-handed,  Ikh. 
d    Negative  Left-handed,  hkl. 
(29).  II.  Pentagonal  Icositetrahedral  Class,  Plagi- 
hedral  Hemihedral  Class,  Plagihedral  Group,  Gyroidal 
Hemihedral    Class,    Gyroidal    Group,   Class    of    the 
Gyroid.     See  pages  138,  166  ;  Fig.  606. 
Forms : 

1.  Hexahedron  or  Cube,  100. 

2.  Dodecahedron,  110. 

3.  Octahedron,  111. 

4.  Tetrakis  Hexahedron,  hkO. 

5.  Tetragonal  Triakis  Octahedron,  hll 

6.  Trigonal  Triakis  Octahedron,  hhl. 

7.  Pentagonal  Icositetrahedron  : 

a.  Right-handed,  hkl. 

b.  Left-handed,  Ikh. 

(30).  III.  Dyakis  Dodecahedral  Class,  Parallel 
Hemihedral  Class,  Pentagonal  Hemihedral  Class, 
Pyritohedral  Group,  Pyritohedral  Hemihedral  Group, 
Class  of  the  Diploid.  See  pages  135,  166  ;  Fig.  605. 

Forms : 

1.  Hexahedron  or  Cube,  100. 

2.  Dodecahedron,  110. 

3.  Octahedron,  111. 


THE    THIRTY-TWO    CLASSES    OF    CRYSTALS.          185 

4.  Pentagonal  Dodecahedron  : 

a.  Right-handed,  hkQ. 

b.  Left-handed,  khQ. 

5.  Tetragonal  Triakis  Octahedron,  hll. 

6.  Trigonal  Triakis  Octahedron,  hhl. 

7.  Dyakis  Dodecahedron  : 

a.  Right-handed,  hkl. 

b.  Left-handed,  kill. 

(31).  IV.  Hexakis  Tetrahedral  Class,  Inclined 
Hemihedral  Class,  Inclined-Faced  Hemihedral  Class, 
Tetrahedral  Group,  Tetrahedral  Hemihedral  Class, 
Class  of  the  Hextetrahedron,  Hextetrahedral  Class, 
Oblique  Hemihedral  Class.  See  pages  131,  165  ;  Fig. 
604. 

Forms : 

1.  Hexahedron  or  Cube,  100. 

2.  Dodecahedron,  110. 

3.  Tetrahedron  : 

a.  Positive,  111. 

b.  Negative,  111. 

4.  Tetrakis  Hexahedron,  hkO. 

5.  Tetragonal  Triakis  Tetrahedron  : 

a.  Positive,  hhl. 

b.  Negative,  hhl. 

6.  Trigonal  Triakis  Tetrahedron  : 

a.  Positive,  hll. 

b.  Negative,  hll. 


186  NOTES    ON    CRYSTALLOGRAPHY. 

7.  Hexakis  Tetrahedron : 

a.  Positive,  hkl. 

b.  Negative,  hkl. 

(32).  V.  Hexakis  Octahedral  Class,  Holohedral 
Class,  Normal  Group,  Class  of  the  Hexoctahedron, 
Hexoctahedral  Class.  See  pages  125,  165  ;  Fig.  603. 

Forms  : 

1.  Hexahedron  or  Cube,  100. 

2.  Dodecahedron,  110. 

3.  Octahedron,  111. 

4.  Tetrakis  Hexahedron,  hkQ. 

5.  Tetragonal  Triakis  Octahedron,  Jill. 

6.  Trigonal  Triakis  Octahedron,  hhl. 

7.  Hexakis  Octahedron,  hkl. 


CHAPTER  XII 

CRYSTALLOGRAPHIC    NOMENCLATURE 

THE  names  in  Crystallography  are  undoubtedly  a 
serious  stumbling-block  to  most  students,  yet  in  point 
of  fact  crystals  are  named  in  a  way  that  is  very  similar 
to  that  in  which  men  are  named  the  world  over. 
Again,  the  crystallographic  names  are  no  more  diffi- 
cult to  pronounce  than  are  the  names  of  persons  of 
one  nationality  to  those  of  different  nations  and  speech. 
Foreigners  make  havoc  with  our  proper  names,  and 
we  have  difficulty  in  learning  how  to  pronounce  the 
names  of  the  emigrants  who  come  to  our  shores  from 
Russia,  Poland,  and  Bohemia. 

The  object  of  applying  a  name  to  an  individual, 
variety  or  species  is  to  distinguish  it  absolutely  from 
all  others.  When  men  live  in  comparatively  small 
communities  and  each  individual  leads  a  somewhat 
stationary  life,  one  name  has  been  generally  found 
sufficient ;  every  one  is  known  amongst  his  fellows  as 
Smith,  Brown  or  Jones,  or,  it  may  be,  as  William, 
Robert,  John  or  James.  When  men  live  in  larger 
communities,  or  intermingle  freely  as  a  result  of  polit- 

(187) 


188  NOTES    ON    CRYSTALLOGRAPHY. 

ical  commotions  or  the  increased  facilities  for  travel,  a 
necessity  arises  for  binomial,  or  trinomial,  or  even 
longer  names. 

When  several  individuals  of  the  same  name  were 
associated  together,  some  other  term  than  that  of  the 
family  name  was  necessary  to  distinguish  each  one 
from  his  fellows.  Accordingly,  for  the  sake  of  dis- 
tinction, to  a  man's  given  name  was  added  a  nick- 
name referring  frequently  to  some  personal  pecu- 
liarity, as,  e.  g.,  Red  Angus,  Black  Douglas  or  Fred- 
erick Barbarossa.  Later,  a  secondary  name,  without 
any  peculiar  personal  significance,  was  attached  to  a 
man's  family  name,  as,  e.  g.,  William  Shakespeare, 
John  Milton  or  Ben  Johnson.  Later  it  became  neces- 
sary or  desirable  to  add  one  or  several  middle  names, 
as,  e.  g.,  Henry  Wadsworth  Longfellow,  Josiah  Dmght 
Whitney  and  Louis  Jean  Rudolphe  Agassiz ;  and  thus 
the  modern  method  of  personal  nomenclature  has 
been  developed. 

In  the  nomenclature  of  Crystallography  the  student 
can  observe  a  marked  resemblance  to  the  system  fol- 
lowed in  the  naming  of  persons.  He  can  notice  the 
single  name  in  the  Octahedron  ;  the  nickname  in  the 
Cube  and  Gyroid,  the  family  names  in  the  Pinacoids, 
Pyramids,  and  Prisms ;  the  double  names  in  the 
Dyakis  Dodecahedron  and  the  Hexakis  Octahedron  ; 
the  trinomial  names  in  the  Trigonal  Triakis  Octa- 
hedron, Primary  Hexagonal  Pyramid,  and  others. 


CRYSTALLOGRAPHIC    NOMENCLATURE.  189 

The  resemblance  to  personal  nomenclature  can  be 
well  seen  in  the  case  of  the  various  tribes  and  families 
of  Prisms,  Pyramids,  and  Pinacoids,  and  in  the 
Isometric  System. 

The  change  of  one  family  name  to  another,  as  is 
common  amongst  men,  is  observed  in  the  Domes 
which  are  in  truth  Prisms.  Again,  the  various  Tri- 
gonal Prisms  are  descended  from  the  various  Hex- 
agonal Prisms,  and  the  Sphenoids  from  the  Pyramids, 
as  are  also  the  Trapezohedrons,  Rhombohedrons,  and 
Scalenohedrons.  In  the  Isometric  Tribe  can  be  found 
the  families  of  the  Tetrakis  Hexahedrons  and  Octa- 
hedrons, with  their  various  descendants. 

It  is  thought  that  the  tabulation  given  below,  which 
associates  the  related  forms  and  enumerates  many  of 
their  names,  will  furnish  the  observant  student  with  a 
new  method  of  retaining  in  his  memory  the  true  rela- 
tionship of  the  various  forms. 

W.  THE  FAMILIES  OF  THE  PRISM  TRIBE 

A.    THE    FAMILY  OF  TRICLINIC    PRISMS 

I.  Triclinic  Hemi  Vertical  Prism,*  alias  Triclinic 
Hemi  Vertical  Dome,  Hemi  Prism,  Vertical  Prism, 
Triclinohedral  Prism,  Klinorhombohedral  Prism,  etc. 

*  In  these  lists  the  names  used  chiefly  in  this  book  are  printed  in 
heavy-faced  type. 


190  NOTES    ON    CRYSTALLOGRAPHY. 

II.  Triclinic   Hemi  Brachy  Prism,   alias  Triclinic 
Hemi   Brachy  Dome,   Hemi    Brachy   Dome,   Brachy 
Dome,  Horizontal  Prism,  Second   Horizontal  Prism, 
Hemi  Dome,  etc. 

III.  Triclinic  Hemi  Macro   Prism,   alias  Triclinic 
Hemi  Macro  Dome,  Hemi  Macro  Dome,  Macro  Dome, 
Horizontal    Prism,    First    Horizontal    Prism,    Hemi 
Dome,  etc. 

B.    THE  FAMILY  OF  MONOCLINIC  PRISMS 

I.  Monoclinic  Vertical  Prism,  alias  Monoclinic  Ver- 
tical Dome,  Vertical  Prism,  Oblique  Rhombic  Prism, 
Rhombic  Prism,  etc. 

II.  Monoclinic  Clino  Prism,  alias  Monoclinic  Glino 
Dome,  Clino  Dome,  Clino  Diagonal  Prism,  Horizontal 
Prism,  Horizontal  Prism  of  a  Rhombohedral  Section. 

III.  Monoclinic   Hemi    Ortho   Prism,   alias  Mono- 
clinic  Hemi  Ortho  Dome,  Hemi  Ortho  Dome. 

C.    THE  FAMILY  OF  ORTHORHOMBIC  PRISMS 

I.  Orthorhombic  Vertical  Prism,  alias  Orthorhombic 
Vertical  Dome,  Vertical  Prism,  Rhombic  Prism,  Ver- 
tical Rhombic  Prism,  Oblique  Angled  Quadralateral 
Prism,  Vertical  Quadralateral  Prism,  etc. 

II.  Orthorhombic  Brachy  Prism,  alias  Orthorhom- 
bic Brachy  Dome,  Brachy  Dome,  Brachy  Diagonal 
Dome,   Brachy    Diagonal    Prism,    Horizontal    Prism, 
Second  Horizontal  Prism,  etc. 


CRYSTALLOGRAPHIC   NOMENCLATURE.  191 

III.  Orthorhombic  Macro  Prism,  alias  Orthorhom- 
bic  Macro  Dome,  Macro  Dome,  Macro  Diagonal  Dome, 
Macro  Diagonal  Prism,  Horizontal  Prism,  First  Hori- 
zontal Prism,  etc. 

D.    THE  FAMILY  OF  TETRAGONAL  PRISMS 

I.  Primary  Prism,  alias  Direct  Prism,  Unit  Prism, 
Prism  of  the  First  Order,  Quadratic  Prism,  Tetragonal 
Prism  of  the  First  Order,  Primary  Tetragonal  Prism, 
Direct  Tetragonal  Prism,  etc. 

II.  Secondary  Prism,  alias  Inverse  Prism,  Diamet- 
ral  Prism,  Prism  of  the  Second    Order,  Secondary 
Tetragonal  Prism,  Inverse  Tetragonal  Prism,  Quad- 
ratic Prism,  Tetragonal  Prism  of  the  Second  Order, 
etc. 

III.  Di   Tetragonal   Prism,    alias    Di   Octahedral 
Prism,  Octagonal  Prism,  etc. 

1.  Hemi  Di  Tetragonal  Prism,  alias  Tertiary 
Prism,  Prism  of  the  Third  Order,  Tetragonal 
Prism  of  the  Third  Order. 

E.   THE  FAMILY  OF  HEXAGONAL  PRISMS 

I.  Primary  Hexagonal  Prism,  alias  Hexagonal 
Prism  of  the  First  Order,  Unit  Prism,  Regular  Hexa- 
gonal Prism,  Hexagonal  Prism  of  the  Principal 
Series,  First  Hexagonal  Prism,  etc. 


192 


NOTES    ON    CRYSTALLOGRAPHY. 


1.  Henri  Primary  Hexagonal  Prism,  alias  Pri- 
mary Trigonal  Prism,  Trigonal  Prism,  etc. 

a.  Positive  Primary  Trigonal  Prism. 

b.  Negative  Primary  Trigonal  Prism. 

II.  Secondary  Hexagonal  Prism,  alias  Hexagonal 
Prism  of  the  Second  Order,  Diagonal  Prism,  Regular 
Hexagonal  Prism,  Second  Hexagonal  Prism,  Hexa- 
gonal Prism  of  the  Second  Series. 

1.  Henri  Secondary  Hexagonal  Prism,  alias  Sec- 
ondary Trigonal  Prism,  Prism  of  the  Second 
Order. 

a.  Positive  or  Right-Handed  Trigonal  Prism. 

b.  Negative  or  Left-Handed  Trigonal  Prism. 

III.  Di   Hexagonal    Prism,    alias    Do    Decagonal 
Prism,  Twelve-sided  Prism,  etc. 

1.  Henri    Di   Hexagonal   Prism,    alias   Tertiary 
Hexagonal  Prism,   Hexagonal   Prism   of  the 
Third  Order. 

a.  Positive  or  Right-Handed  Hexagonal  Prism. 

b.  Negative  or  Left-Handed  Hexagonal  Prism. 

2.  Hemi  Di  Hexagonal  Prism,  alias  Primary  Di 
Trigonal  Prism,  Di  Trigonal  Prism  of  the  First 
Order. 

a.  Positive  Di  Trigonal  Prism. 

b.  Negative  Di  Trigonal  Prism. 

3.  Hemi  Di  Hexagonal  Prism,  alias  Secondary 


CRYSTALLOGRAPHIC    NOMENCLATURE.  193 

Di  Trigonal  Prism,  Di  Trigonal  Prisin  of  the 
Second  Order. 

a.  Right-Handed  Di  Trigonal  Prism. 

b.  Left-Handed  Di  Trigonal  Prism. 

4.  Tetarto  Di  Hexagonal  Prism,  alias  Tertiary 
Trigonal  Prism,  Trigonal  Prism  of  the  Third 
Order. 

a.  Positive    Eight-Handed    Tertiary    Trigonal 

Prism. 

b.  Positive     Left- Handed     Tertiary     Trigonal 

Prism. 

c.  Negative    Right-Handed    Tertiary    Trigonal 

Prism. 

d.  Negative     Left- Handed     Tertiary     Trigonal 

Prism. 

X.  THE  FAMILIES  OF  THE  PYRAMID  TRIBE 

A.   THE  FAMILY  OF  TRICLINIC  PYRAMIDS 

I.  Triclinic  Tetarto  Pyramid,  alias  Triclinic  Pyra- 
mid, Clinorhombic  Octahedron,  etc.  Nicknames,  An- 
orthotype,  Anorthoid. 

B.   THE  FAMILY  OF  MONOCLINIC  PYRAMIDS 

I.  Monoclinic  Hemi  Pyramid,  alias  Monoclinic  Pyr- 
amid, etc.     Nicknames,  Augitoid,  Hemiorthotype. 
13 


194  NOTES   ON    CRYSTALLOGRAPHY. 

0.  THE   FAMILY  OF  ORTHORHOMBIC   PYRAMIDS 

I.  Orthorhombic  Pyramids,  alias  Rhombic  Pyramid, 

Rhombic  Pyramidohedron,  Rhombic  Octahedron,  Or- 
thorhombic Octahedron,  etc.     Nickname,  Orthotype. 

1.  Orthorhombic    Hemi   Pyramid,    alias   Ortho- 
rhombic  Sphenoid,  Sphenoid,  Rhombic  Sphe- 
noid,  Rhombic    Sphenoidohedron,    Rhombic 
Tetrahedron,  Irregular  Tetrahedron,  etc.    Nick- 
name, Tartartoid  : 

a.  Positive     or     Right-handed     Orthorhombic 

Sphenoid. 

b.  Negative  or  Left-handed  Orthorhombic  Sphe- 

noid. 

D.  THE  FAMILY  OF  TETRAGONAL  PYRAMIDS 

I.  Primary  Tetragonal  Pyramid,  alias  Primary  Pyr- 
amid, Direct  Tetragonal  Pyramid,  Direct  Pyramid, 
Unit  Pyramid,  Tetragonal  Pyramid  of  the  First  Order, 
Pyramid  of  the  Unit  Order,  Pyramid  of  the  First 
Order,  Direct  Octahedron,  Quadratic  Octahedron, 
Quadratic  Octahedron  of  the  First  Order,  Pyramid 
Octahedron  of  the  First  Order,  Tetragonal  Pyramido- 
hedron of  the  First  Direction,  Quadratic  Octahedron 
of  the  First  Series. 

1.  Hemi  Tetragonal  Pyramid,   alias  Tetragonal 

Sphenoid,  Sphenoid,  Quadratic  Tetrahedron, 

Irregular  Tetrahedron : 


CRYSTALLOGRAPHIC    NOMENCLATURE.  195 

a.  Positive  Sphenoid. 

b.  Negative  Sphenoid. 

II.  Secondary  Tetragonal  Pyramid,  alias  Secondary 
Pyramid,  Inverse  Tetragonal  Pyramid,  Inverse  Pyr- 
amid, Diametral  Pyramid,  Trigonal  Pyramid  of  the 
Second  Order,  Pyramid  of  the  Second  Order,  Inverse 
Octahedron,  Quadratic   Octahedron,  Quadratic  Octa- 
hedron of  the  Second  Order,  Quadratic  Octahedron  of 
the  Second  Series,  Tetragonal  Pyramidohedron  of  the 
Second  Direction,  Pyramid  of  the  Diametral  Order, 
Quadratic  Pyramid,  etc. 

III.  Di  Tetragonal  Pyramid,  alias  Di  Tetragonal 
Octahedron,  Di  Octahedron,  Di  Tetragonal  Pyramid 
of  the  First  Direction.     Nickname,  Zirconoid. 

1.  Hemi  Di  Tetragonal  Pyramid,  alias  Tertiary 
Tetragonal  Pyramid,  Tertiary  Pyramid,  Tetra- 
gonal Pyramid  of  the  Third  Order,  Pyramid 
of  the  Third  Order,  Hemi  Di  Octahedron  : 

a.  Positive  Tertiary  Pyramid. 

b.  Negative  Tertiary  Pyramid. 

2.  Hemi  Di    Tetragonal    Pyramid,   alias   Tetra- 
gonal Scalenohedron,  Di  Tetragonal  Scaleno- 
hedron.      Nickname,    Disphene,    Diplo  Tetra- 
hedron : 

a.  Positive  Tetragonal  Scalenohedron. 

b.  Negative  Tetragonal  Scalenohedron. 


196  NOTES    ON    CRYSTALLOGRAPHY. 

3.  Hemi  Di  Tetragonal  Pyramid,  alias  Tetra- 
gonal Trapezohedron,  Quadratic  Trapezo- 
hedron,  Trapezoidal  Octahedron,  etc.: 

a.  Positive  or  Eight-handed  Tetragonal  Trapezo- 

hedron. 

b.  Negative  or  Left-handed  Tetragonal  Trapezo- 

hedron. 

E.    THE    FAMILY    OF    HEXAGONAL    PYRAMIDS 

I.  Primary  Hexagonal  Pyramid,  alias  Hexagonal 
Pyramid  of  the  First  Order,  Di  Hexahedron  of  the 
Principal   Series,    Hexagonal    Dodecahedron    of    the 
First  Order,  Right  Angled  Dodecahedron,  Hexagonal 
Pyramid  of  the  First  Division,  Hexagonal  Pyramido- 
hedron  of  -the  First  Normal  Direction,  Quartzoid  of 
the  First  Order,  etc.     Nickname,  Quartzoid. 

1.  Hemi    Primary    Hexagonal    Pyramid,    alias 
Rhombohedron,   Primary    Rhombohedron, 
Rhombohedron   of    the   First    Order,    Eight- 
Angled    Hexahedron,   Rhombohedron    of  the 
Principal  Series,  Hemi  Dodecahedron  of  the 
First  Order,   Rhombohedron   of  the  Vertical 
Primary  Zone. 

2.  Hemi  Primary  Hexagonal  Pyramid,  alias  Pri- 
mary Trigonal  Pyramid,  Trigonal  Pyramid  of 
the  First  Order. 

II.  Secondary  Hexagonal  Pyramid,  alias  Hexagonal 


CRYSTALLOGRAPHIC    NOMENCLATURE.  197 

Pyramid  of  the  Second  Order,  Di  Hexahedron  of  the 
Second  Order,  Di  Hexahedron  of  the  Principal  Series, 
Hexagonal  Dodecahedron  of  the  Second  Order,  Eight- 
Angled  Dodecahedron,  Hexagonal  Pyramid  of  the 
Second  Division,  Hexagonal  Pyramidohedron  of  the 
Second  Normal  Direction,  Quartzoid  of  the  Second 
Order,  etc.  Nickname,  Quartzoid. 

1.  Hemi   Secondary   Hexagonal    Pyramid,   alias 
Secondary  Rhombohedron,  Rhombohedron  of 
the  Second  Order,  etc. 

a.  Positive  Secondary  Rhombohedron  or  Posi- 

tive Rhombohedron  of  the  Second  Order. 

b.  Negative  Secondary  Rhombohedron  or  Nega- 

tive Rhombohedron  of  the  Second  Order. 

2.  Hemi   Secondary    Hexagonal    Pyramid,   alias 
Secondary  Trigonal  Pyramid,  Trigonal  Pyra- 
mid of  the  Second  Order. 

a.  Positive  or  Right-Handed  Trigonal  Pyramid. 

b.  Negative  or  Left-Handed  Trigonal  Pyramid. 
III.  Dihexagonal  Pyramid,  alias  Di  Dodecahedron. 

Nickname,  Berylloid. 

1.  Hemi  Di  Hexagonal  Pyramid,  alias  Hexa- 
gonal Scalenohedron,  Scalenohedron,  Di  Hex- 
agonal Scalenohedron,  Hemi  Dodecahedron, 
Bi  Pyramid.  Nickname,  Calcite  Pyramid. 

a.  Positive  Scalenohedron. 

b.  Negative  Scalenohedron. 


198  NOTES    ON    CRYSTALLOGRAPHY. 

2.  Hemi  Di  Hexagonal  Pyramid,  alias  Tertiary 
Hexagonal  Pyramid,  Hexagonal  Pyramid  of 
the  Third  Order,  Di  Hexagonal  Hemi  Di  Do- 
decahedron, Hemihedral  Di  Hexahedron. 

a.  Positive  or  Right-Handed  Tertiary  Hexagonal 

Pyramid. 

b.  Negative  or  Left-Handed  Tertiary  Hexagonal 

Pyramid. 

3.  Hemi  Di  Hexagonal  Pyramid,  a  lias  Hexagonal 
Trapezohedron,  Di  Hexagonal  Trapezohedron, 
Trapezoid    Di    Hexahedron.     Nickname,    Di- 
plagihedron. 

a.  Right-Handed  Hexagonal  Trapezohedron. 

b.  Left- Handed  Hexagonal  Trapezohedron. 

4.  Tetarto  Di  Hexagonal  Pyramid,  alias  Hemi 
Hexagonal  Scalenohedron,  Tertiary  Rhombo- 
hedron,  Rhombohedron  of  the  Third  Order. 

a.  Positive  Right-Handed  Tertiary  Rhombohe- 

dron. 

b.  Negative  Right-Handed  Tertiary  Rhombohe- 

dron. 

c.  Positive    Left-Handed    Tertiary   Rhombohe- 

dron. 

d.  Negative   Left-Handed  Tertiary   Rhombohe- 

dron. 

5.  Tetarto  Di  Hexagonal  Pyramid,  alias  Di  Tri- 
gonal Pyramid. 


CRYSTALLOGRAPHIC    NOMENCLATURE.  199 

a.  Positive  Di  Trigonal  Pyramid. 

b.  Negative  Di  Trigonal  Pyramid. 

6.  Tetarto  Di  Hexagonal  Pyramid,  alias   Hemi 
Hexagonal  Scalenohedron,  Trigonal  Trapezo- 
hedron,   Di  Trigonal  Trapezobedron,  Trigon 
Trapezohedron.     Nickname,  Plagihedron : 

a.  Positive    Eight-handed    Trigonal    Trapezo- 

hedron. 

b.  Negative    Right-handed    Trigonal    Trapezo- 

hedron. 

c.  Positive  Left-handed  Trigonal  Trapezohedron. 

d.  Negative     Left-handed     Trigonal     Trapezo- 

hedron. 

7.  Tetarto  Di  Hexagonal  Pyramid,  alias  Tertiary 
Trigonal  Pyramid,  Trigonal  Pyramid  of  the 
Third  Order : 

a.  Positive    Eight-handed     Tertiary    Trigonal 

Pyramid. 

b.  Negative    Right-handed    Tertiary    Trigonal 

Pyramid. 

c.  Positive  Left- handed  Tertiary  Trigonal  Pyr- 

amid. 

d.  Negative  Left-handed  Tertiary  Trigonal  Pyr- 

amid. 

Y.    THE  FAMILIES  OF  THE  PINACOID  TRIBE 
I.  Basal  Pinacoid,  alias  Vertical   Pinacoid,    Basal 
Plane,  Base,  End  Plane,  etc. 


200  NOTES    ON    CRYSTALLOGRAPHY. 

II.  Brachy  Pinacoid,  alias   Brachy  Diagonal  Pin- 
acoid. 

III.  Macro  Pinacoid,  alias  Macro  Diagonal  Pinacoid. 

IV.  Clino  Pinacoid. 

V.  Ortho  Pinacoid. 

Z.    THE  FAMILIES  OF  THE  ISOMETRIC  TRIBE 

I.  Hexahedron.     Nickname,  Cube. 

II.  Dodecahedron,   alias  Rhombic   Dodecahedron, 
Regular    Rhombic    Dodecahedron,    etc.      Nicknames, 
Garnet    Crystallization,    Garnetohedron,     Garnetoid, 
Garnet  Dodecahedron. 

III.  Tetrakis  Hexahedron,  alias  Tetra  Hexahedron, 
Hexahedral  Trigonal  Icosi   Tetrahedron,   Pyramidal 
Cube,  etc.     Nickname,  Fluoroid. 

1.  Hemi  Tetrakis  Hexahedron,  alias  Pentagonal 
Dodecahedron,  Hexahedral  Pentagonal  Dode- 
cahedron, Dornatic  Dodecahedron,  etc.  Nick- 
names, Pyrite  Dodecahedron,  Pyritohedron, 
Pyritoid. 

IV.  Octahedron,  alias  Regular  Octahedron,  Regular 
Four-sided  Double  Pyramid,  etc. 

1.  Hemi  Octahedron,  alias  Tetrahedron,  Regular 
Tetrahedron,  etc. 

V.  Trigonal  Triakis  Octahedron,  alias  Triakis  Octa- 
hedron, Tris  Octahedron,  Pyramid  Octahedron,  Octa- 
hedral Trigonal   Icosi  Tetrahedron,  Octahedral  Pyr- 
amidal Icosi  Tetrahedron.     Nickname,  Galenoid. 


CRYSTALLOGRAPHIC    NOMENCLATURE.  201 

1.  Hemi  Trigonal  Triakis  Octahedron,  alias 
Tetragonal  Triakis  Tetrahedron,  Tetragonal 
Tris  Tetrahedron,  Tris  Tetrahedron,  Deltoid 
Dodecahedron,  Tetragonal  Dodecahedron, 
Trapezoidal  Dodecahedron,  Deltohedron,  Trap- 
ezoid  Tetrahedron,  etc. 

VI.  Tetragonal  Triakis  Octahedron,  alias  Trapezo- 
hedron,  Icosi  Tetrahedron,  Trapezoidal  Icosi  Tetra- 
hedron, Deltoid   Icosi  Tetrahedron,   etc.     Nicknames, 
Leucite  Crystallization,  Leucitohedron,  Leucitoid. 

1.  Hemi  Tetragonal  Triakis  Octahedron,  alias 
Trigonal  Triakis  Tetrahedron,  Triakis  Tetra- 
hedron, Pyramidal  Tetrahedron,  Trigonal 
Dodecahedron,  Pyramidal  Dodecahedron, 
Hemi  Icosi  Tetrahedron,  etc.  Nickname, 
Cuproid. 

VII.  Hexakis  Octahedron,  alias  Hex  Octahedron, 
Octakis  Hexahedron,  Trigonal  Polyhedron,  Pyramidal 
Garnetohedron,  etc.     Nickname,  Adamantoid. 

1.  Hemi  Hexakis  Octahedron,  alias  Hexakis  Tet- 
rahedron, Trigonal  Icosi  Tetrahedron,  Tetra- 
hedral  Trigonal  Icosi  Tetrahedron,  etc*     Nick- 
name, Boracitoid. 

2.  Hemi  Hexakis  Octahedron,  alias  Dyakis  Do- 
decahedron, Hemi  Octakis  Hexahedron,  Tet- 
ragonal   Icosi   Tetrahedron,    Trapezoid    Icosi 
Tetrahedron,  Trapezoid  Di  Dodecahedron,  etc. 


202  NOTES    ON    CRYSTALLOGRAPHY. 

Nicknames,  Diploid,  Diplo-Pyritohedron,  Diplo- 
Pyritoid,  Diplohedron,  etc. 

3.  Hemi  Hexakis  Octahedron,  alias  Pentagonal 
Icosi  Tetrahedron.     Nickname,  Gyroid. 

4.  Tetarto  Hexakis  Octahedron,  alias  Tetrahedral 
Pentagonal  Dodecahedron.     Nickname,  Tetar- 
toid. 


DESCRIPTIONS  OF  THE  PLATES 


PLATE   I 

PAGE 

Fig.  1.  Triclinic  Axes  with  Semi-Axial  Notation,  7,  9, 10, 29,  33 
Fig.  2.  Monoclinic  Axes  with  Semi-Axial  Notation,  7, 40-42, 47 
Fig.  3.  Orthorhombic  Axes  with  Semi- Axial  Notation, 

7,50,51,57 

Fig.  4.  Tetragonal  Axes  with  Semi-Axial  Notation  .  .  .  .  7,  60 
Fig.  5.  Isometric  Axes  with  Semi-Axial  Notation  .  .  7, 122, 126 
Fig.  6.  Hexagonal  Axes  with  Semi- Axial  Notation,  8,  73,  75, 109 
Fig.  7.  Orthorhombic  Pyramid  (111),  with  the  Axes  drawn 

in.     Sulphur 7,  25,  51 

Fig.  8.  Monoclinic  Crystal  showing  Plane  of   Symmetry 

(A  B  C  D)  and  Axis  of  Binary  Symmetry.    Forms :  Clino- 

Pinacoid    (010);    Prism    (110),    and    Clino-Dome  (Oil). 

Natron 8,11,12,17,18,26,41,44,46,47 

Fig.  9.  Monoclinic  Crystal  showing  Plane  of    Symmetry 

(A  B  C  D)  and  Axis  of  Binary  Symmetry.  Forms  :  Clino- 

Pinacoid  (010);   Prism   (110),  and  a  Clino-Dome   (Oil). 

Gypsum  .........  3,  11,  12,  15,  17,  18,  26,  41,  44,  46,  47 

Fig.  10.  Monoclinic  Crystal  showing  Plane  of  Symmetry 

(A  B  C  D  H)  and  Axis  of  Binary  Symmetry  (A  C). 

Forms:  Clino-Pinacoid  (010);  Prism  (110);  Clino-Dome 

(Oil),  and  a  Hemi-Pyramid  (111).    Gypsum, 

3, 11,  12,  15,  17,  18,  26,  41,  44,  46,  47 
Fig.  11.  Monoclinic  Crystal  showing  Plane  of  Symmetry 

(A  B  C  D)  and  Axis  of  Binary  Symmetry.    Forms: 

Clino-Pinacoid   (6  or  010);    Ortho-Pinacoid   (r  or  100); 

Prism  (M or  110),  and  Clino  Dome  (s  or  Oil).     Augite, 

17,  18,  26,41,  44,46 
(203) 


204  DESCRIPTIONS   OF    THE    PLATES. 

PAGE 

PLATE  II 

Fig.  12.  Isometric.    Octahedron  (111).    Magnetite, 

3,  14,  23, 123,  128 

Fig.  18.  Isometric.  Octahedron  (111),  distorted  by  being 
shortened  in  the  direction  of  the  Cubic  Axes.  Alum  .  .  3 

Fig.  14.  Isometric.  Octahedron  (111),  distorted  the  same 
as  Fig.  13.  Alum 3 

Fig.  15.  Isometric.  Octahedron  (111 ),  with  its  Solid  Angles 
truncated  by  a  Cube  (100)  Linnseite  ...  3, 14, 23,  26,  123, 141 

Fig.  16.  Isometric.  Octahedron  (111),  distorted  the  same 
as  Fig.  13  and  modified  by  a  Cube  (100).  Chrome  Alum,  3,  26 

Fig.  17.  Isometric.  Octahedron  (111),  with  its  solid  angles 
truncated  by  a  Cube  (100)  and  its  edges  truncated  by  a 
Dodecahedron  (110).  Galenite  ...  3, 14,  23,  26,  27,  123, 141 

Fig.  18.  Isometric.  Octahedron  (111)  modified  by  a  dis- 
torted Cube  (100)  and  a  distorted  Dodecahedron  (110). 
Chrome  Alum 8, 14,  26 

Fig.  19.  Isometric.  Octahedron  (0  or  111),  distorted,  and 
modified  by  a  Cube  ( oo  0  oo  or  100)  and  a  Dodecahedron 
(co  0  or  110).  Chrome  Alum ,,3 

Fig.  20.  Isometric.  Octahedron  (111).  A  curved  and  dis- 
torted form  of  the  Diamond  in  which  the  curved  Faces 
approximate  those  of  an  Octahedron,  or  it  can  be  consid- 
ered a  twin  form ,.  -.$ 

Fig.  21.  Hexagonal.  Distorted.  Primary  Prism  (lOlO) ; 
modified  by  a  Primary  Pyramid  (1011),  or  by  two  Rhom- 
bohedrons :  « <{  loll  }•  and  *  •{  OlTl  }• .  Quartz "f. 

Fig.  22.  Orthorhombic.  Distorted.  Pyramid  (111);  modi- 
fied by  a  second  Pyramid  (112);  a  Prism  (110),  and  a 
Brachy-Pinacoid  (010).  Niter * 

Fig.  23.  Isometric.  Parallel  Growths.  Octahedrons  (111). 
Alum 3, 149 

Fig.  24.  Isometric.  Parallel  Growths.  Octahedrons  (111). 
Alum 3,  149 


DESCRIPTIONS    OF    THE    PLATES. 


205 


Fig.  25.  Tetragonal.  Parallel  Growths,  united  by  Pinacoids 
(001) 3, 149 

Fig.  26.  Hexagonal.  Parallel  Growths.  Primary  Pyramid 
( 1  Oil ),  and  a  Primary  Prism  (1 010).  Quartz  .  .  .  .3,28,149 

Fig.  27.  Hexagonal.  Parallel  Growths.  A  Primary  Pyra- 
mid (lOll)  and  a  Primary  Prism  (lOlO).  Quartz  .  .  .  .  3, 149 

Fig.  28.  Triclinic.  Composed  of  4  Tetarto-Pyramids  (111, 
ill,  111,  111) 13,19-21,25,26,33,34,44 

Fig.  29.  Triclinic.  A  Compound  Crystal  showing  a  Tetarto- 
Pyramid  (ill);  a  Hemi-Prism  (llo);  and  a  Macro-Pina- 
coid(lOO).  Axinite 12,13,19-21,25,26,33,34,44 

Fig.  30.  Triclinic.  A  Compound  Crystal  showing  three 
Tetarto-Pyramids  (111,  221,  311);  one  Hemi-Prism  (HO); 
a  Hemi  Macro-Dome  (021);  and  a  Macro-Pinacoid  (100). 
Axinite  12,13,19-21,25,26,33,34,44 

Fig.  31.  Triclinic.  A  Compound  Crystal  showing  a  Tetarto- 
Pyramid  (111);  two  Hemi-Prisms  (110,  flO);  a-Hemi- 
Macro  Dome  (101);  a  Basal  Pinacoid  (OOl),  and  a  Brachy- 
Pinacoid  (010).  Albite  .  .  .  .12,13,19-21,25,26,33,34,44 

Fig.  32.  Triclinic.  A  Compound  Crystal  showing  four 
Tetarto-Pyramids  (111,  ill,  111,  111);  two  Hemi-Prisms 
(110,  HO);  a  Brachy-Pinacoid  (010),  and  a  Macro-Pina- 
coid (100).  Chalcanthite  ....  12,  13,  19-21,  25,  26, 33, 34,  44 

Fig.  33.  Triclinic.  A  Compound  Crystal,  composed  of  two 
Hemi-Prisms  (110  and  HO);  two  Basal  Pinacoids  (001  and 
001);  a  Brachy-Pinacoid  (010),  and  a  Macro-Pinacoid 
(100) 11,12,19-21,26,33,34,44 

Fig.  34.  Triclinic.  A  Compound  Crystal  showing  two  Tet- 
arto-Pyramids (111,  2Pi  or  121):  six  Hemi-Prisms  (110, 
110, 101,  102,  'Pt  oo  or  011,2'P,  oo  or  021);  a  Basal  Pina- 
coid (001);  a  Brachy-Pinacoid  (010);  and  a  Macro-Pina- 
coid (100).  Chalcanthite  .  .  .  .12, 13,  19-21,  25,  26,  33,  34,  44 


206  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

PLATE  III 

Fig.  35.  Triclinic.  Compound  Crystal  showing  a  Tetarto- 
Pyramid  (111);  two  Hemi-Prisms  (110,  llo);  a  Brachy- 
Pinacoid  (010),  and  a  Macro-Pinacoid  (100).  Chalchan- 
thite 12,13,19-21,25,26,33,34,44 

Fig.  36.  Hexagonal.  Compound  Form  composed  of  a  Pri- 
mary Pyramid  (1011),  and  a  Primary  Prism  (10TO). 
Quartz -18,26,74,76,81,83,104 

Fig.  37.  Hexagonal.  Compound  Form  composed  of  a  Pri- 
mary Prism  (lOK)),  a  Primary  Pyramid  (1011);  a  Second- 
ary Pyramid  (1121),  and  Basal  Pinacoids  (0001,  OOOl). 
Apatite 18,26,74,76,80-83,104 

Fig.  38.  Hexagonal.  Compound  Form  composed  of  a  Pri- 
mary Prism  (1010);  a  Primary  Pyramid  (1011),  and  Basal 
Pinacoids  (0001,  0001).  Apatite  ...  18,  26,  74,  76,  80-83, 104 

Fig.  39.  Hexagonal.  Compound  Form  composed  of  a  Pri- 
mary Pyramid  (1011),  and  Basal  Pinacoids  (0001,  OOoT). 
Apatite 18,  26,  74,  76,  80-83,  104 

Fig.  40.  Hexagonal.  Compound  Form  composed  of  a  Pri- 
mary Prism  (1010),  modified  by  a  Secondary  Pyramid 
(1122)  and  a  Dihexagonal  Pyramid  (hkil), 

18,  26,  74,  76,  81-83,  104 

Fig.  41.  Tetragonal.  Compound  Form  composed  of  a  Pri- 
mary Prism  (110)  terminated  by  a  Primary  Pyramid  (111). 
Zircon ......  18,  26,  70,  73,  74 

Fig.  42.  Tetragonal.  Compound  Form  composed  of  a  Pri- 
mary Pyramid  (111)  and  a  Secondary  Prism  (100).  Zircon, 

18,  26,  70,  73,  74 

Fig.  43.  Tetragonal.  Compound  Crystal.  Composed  of  a 
Primary  Prism  (110);  a  Primary  Pyramid  (111),  and  a 
Secondary  Pyramid  (201).  Zircon 18,  26,  70,  73,  74 

Fig.  44.  Tetragonal.  Compound  Form.  Composed  of  a 
Primary  Pyramid  (111);  a  Ditetragonal  Pyramid  (hkl  or 
311)  and  a  Secondary  Prism  (100).  Zircon  .  .  18,  26,  70,  73,  74 


DESCRIPTIONS    OF    THE    PLATES.  207 

PAGE 

JMJJT.  45.   Hexagonal.    A  Positive  Primary  Rhombohedron 

K  <{  2021  }•  modified  by  a  Negative  Primary  lihombohedron 

A- •{0111}-.     Calcite        . 18,26,74,76,87,88,104 

Fig.  46.    Hexagonal.    A  Positive  Primary  Rhombohedron 

«•{  loll  }•  modified  by  Secondary  Hexagonal  Prism  (1120). 

Calcite 18,27,74,76,81,104 

Fig.  47.  Hexagonal.    A  Primary  Rhombohedron  *<{  lOfl  }> , 

modified  by  a  Scalenohedron  K  \  3251  }» .    Calcite, 

18,26,  74,76,81,104 
Fig.  48.   Hexagonal.    A  Scalenohedron  «•{  2131  }> ,  modified 

by  a  Rhombohedron  «•{  loll  }•.    Calcite  .   .  18,  26,  74,  76,  104 
Fig.  49.  Hexagonal.    A  Primary  Prism  (lofo;,  modified  by 

a  Negative  Rhombohedron  «<{  0112  }> .    Calcite, 

18,  26,  74,  76,  81,  104 
Fig.  50.  Hexagonal.    A  Primary  Rhombohedron  « «{  1011  }> 

and  a  Secondary  Prism  (1120).    Calcite  .  18, 26,  74,  76,  81,  104 
Fig.  51.    Qrthorhombic.    Compound   Form    showing    the 

planes  of  a  Vertical  Prism  (110);  a  Brachy-Dome  (Oil); 

Macro-Dome  (101),  and  a  Macro-Pinacoid  (100).    Barite.    26 
Fig.  52.    Isometric.    Positive    Pentagonal    Dodecahedron 

(210).    Pyrite 24,  25,  51,  123,  135,  137 

Fig.  53.    Isometric.    Negative  Pentagonal  Dodecahedron 

(120).    Pyrite 24,25,51,123,135,137 

Fig.  54.    Hexagonal.     Positive     Right-handed     Trigonal 

Trapezohedron,  «r^  hkll  }• 125,76,100,104 

Fig.  55.  Hexagonal.  Positive  Left-handed  Trigonal  Trape- 
zohedron, KT\  ikTd  f  .  .,.  ,..«....  25,  74,  76,  100,  104 

PLATE   IV 

Fig.  56.  Isometric.  Octahedron  (111)  with  its  edges  beveled 
bya  Trigonal  Triakis  Octahedron  (221).  Galenite,  27, 123, 141 

Fig.  57.  Isometric.  Dodecahedron  (110)  with  its  edges 
beveled  by  a  Hexakis  Octahedron  (321).  Garnet .  27, 123,  141 


208  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Fig.  58.  Isometric.  Cube  (100)  with  its  edges  beveled  by 
a  Tetrakis  Hexahedron  (310).  Fluorite 27, 128, 141 

Fig.  59.  Monoclinic.  Compound  Form  showing  a  Prism 
(110);  a  Hemi-Pyramid  (111);  a  Basal  Pinacoid  (001);  a 
Clino-Pinacoid  (010),  and  an  Ortho-Pinacoid  (100).  Py- 
roxene   41-44,  46,  47 

Fig.  60.  Monoclinic.  A  Prism  (110)  with  the  Axes  drawn 
in,  and  terminated  by  Basal  Pinacoids  (001)  .  .  .  41-44,  46,  47 

Fig.  61.  Monoclinic.  Composed  of  Basal  Pinacoids  (001); 
Clino-Pinacoids  (010),  and  Ortho-Pinacoids  (100),  41-44, 46, 47 

Fig.  62.  Monoclinic.  Compound  Form  showing  planes  of 
a  Prism  (110);  a  Positive  Hemi-Ortho-Dome  (101);  a 
Basal  Pinacoid  (001),  and  a  Clino-Pinacoid  (010).  Melan- 
terite  41-47 

Fig.  63.  Monoclinic.  Showing  the  planes  of  a  Prism  (110); 
a  Clino-Dome  (Oil),  and  a  Basal  Pinacoid  (001).  Melan- 
terite .....  41,  47 

Fig.  64.  Monoclinic.  Axes  drawn  in.  Compound  Form 
composed  of  a  Positive  and  a  Negative  Hemi-Pyramid 
(111,111) ..  26,41-47 

Fig.  65.  Monoclinic.  Compound  Form  showing  the  planes 
of  two  Prisms  (110,  120);  a  Clino-Dome  (Oil);  a  Basal 
Pinacoid  (001);  and  a  Clino-Pinacoid  (010) 41-47 

Fig.  66.  Monoclinic.  Compound  Form  composed  of  two 
Prisms  (110,  130);  a  Hemi-Orthodome  (Toi)  and  Basal 
Pinacoids  (001) .  .41-47 

Fig.  67.  Monoclinic.  Compound  Form  showing  Prisms 
(110, 120);  a  Clino-Dome  (Oil);  a  Hemi-Ortho-Dome  (201); 
a  Positive  Hemi-Pyramid  (111),  Clino-Pinacoid  (010),  and 
a  Basal  Pinacoid  (001) 41-47 

Fig.  68.  Monoclinic.  Compound  Form  showing  two  Prisms 
(110,  120);  Positive  and  Negative  Hemi-Pyramids  (111, 
111);  a  Clino-Dome  (Oil);  a  Clino-Pinacoid  (010);  an 
Ortho-Pinacoid  (100),  and  a  Basal  Pinacoid  (001)  .  .  .  41-47 


DESCRIPTIONS    OF    THE    PLATES.  209 

PAGE 

Fig.  69.  MoDOclinic.  Compound  Form  showing  planes  of 
a  Prism  (110),  a  Negative  Henri-Pyramid  (111);  three 
Hemi- Ortho-Domes  (201,  201  and ^401);  a  Basal  Pinacoid 
(001),andaClino-Pinacoid  (010)  ....  ...  ....  .41-47 

Fig.  70.  Monoclinic.  Compound  Form  showing  planes  of 
two  Prisms  (110,  210);  a  Positive-Henri  Pyramid  (111);  a 
Hemi-Ortho-Dome  (101);  a  Clino-Pinacoid  (010);  and  a 
Basal  Pinacoid  (001) -..  *  .  .  .  . 41-47 

Fig.  71.  Monoclinic.  Compound  Form  showing  planes  of 
a  Prism  (110);  a  Hemi-Pyramid  (111);  a  Clino-Pina- 
coid (010),  and  an  Ortho-Pinacoid  (100).  Augite  .  .  41, 43-47 

Fig.  72.  Monoclinic.  Compound  Form  showing  the  planes 
of  a  Prism  (110);  Positive  and  Negative  Henri-Pyramids 
111,  111,  and "221),  and  Clino-,  Ortho-,  and  Basal-Pina- 
coids(010, 100,  001).  Augite 41,43-47 

Fig.  73.  Monoclinic.  Compound  Crystal  showing  planes  of 
two  Prisms  (110,^01);  a  Positive  Pyramid  (Til);  a  Basal 
Pinacoid  (001),  and  an  Ortho-Pinacoid  (100)  .  .  41,  42,  44-47 

Fig.  74.  Monoclinic.  Crystal  showing  planes  of  a  Prism 
(110);  a  Basal  Pinacoid  (001),  and  a  Clino-Pinacoid  (010). 
Sugar 41-47 

Fig.  75.  Monoclinic.  Compound  Crystal  showing  the 
planes  of  a  Prism  (110);  a  Hemi-Ortho  Dome  (Oil);  a 
Clino-Dome  (101);  an  Ortho-Pinacoid  (100),  and  a  Basal 
Pinacoid  (001).  Sugar  .  . 41-47 

Fig.  76.  Monoclinic.  Compound  Form  showing  planes  of 
a  Prism  (110);  a  Positive  Hemi-Pyramid  (111),  and  a 
Basal  Pinacoid  (001) 41-47 

Fig.  77.  Monoclinic.  Compound  Form  showing  planes  of 
a  Prism  (110);  a  Negative  Hemi-Pyramid  (111);  a  Clino- 
Pinacoid  (010),  and  a  Basal  Pinacoid  (001) 41-47 

Fig.  78.  Monoclinic.  Compound  Form  showing  the  planes 
of  two  Henri-Pyramids  (HI,  111);  a  Prism  (T21):  a  Hemi- 


210  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Ortho-Dome  (101);  a  Basal  Pinacoid  (001);  a  Clino-Pina- 
coid  (OlO),  and  an  Ortho-Pinacoid  (100).    Melanterite, 

41,43,44,46,47 

Fig.  79.  Monoclinic.  Compound  Form  showing  planes  of 
a  Prism  (110);  a  Negative  Hemi-Pyramid  (111);  two 
Clino-Domes  (101,  103);  a  Basal  Pinacoid  (001),  and  a 
Clino-Pinacoid  (010).  Melanterite 41,43-47 

Fig.  80.  Monoclinic.  Compound  Crystal  showing  planes  of 
a  Prism  (110).  and  two  Hemi-Pyramids,  (111,  111). 
Gypsum 41,43-47 

Fig.  81.  Monoclinic.  Compound  Crystal  showing  planes  of 
a  Prism  (110);  of  a  Positive  and  a  Negative  Hemi- 
Pyramid  (111,  111),  and  a  Clino-Pinacoid  (010).  Gypsum, 

41,43-47 

Fig.  82.  Monoclinic.  Compound  Form  showing  planes  of 
a  Prism  (110);  two  Hemi-Pyramids  (111,  "221);  a  Basal 
Pinacoid  (001),  and  an  Ortho-Pinacoid  (100).  Borax,  41,  43-47 

Fig.  83.  Monoclinic.  Compound  Form  showing  planes  of 
two  Positive  Hemi-Pyramids  (111,  x  or  221);  a  Basal 
Pinacoid  (001);  a  Clino-Pinacoid  (010),  and  an  Ortho- 
Pinacoid  (100).  Borax 41,  43-47 

Fig.  84.  Monoclinic.  Compound  Form  showing  planes  of 
a  Prism  (110);  a  Clino-Dome  (Oil);  an  Ortho-Dome  (101); 
a  Basal  Pinacoid  (001),  and  an  Ortho-Pinacoid  (100). 
Melanterite 41,  43-47 

Fig.  85.  Monoclinic.  Compound  Form  showing  planes  of 
a  Prism  (110);  a  Negative  Hemi-Pyramid  (111),  three 
Hemi-Ortho-Domes  (Toi,  10l,  103);  a  Basal  Pinacoid 
(001),  and  a  Clino-Pinacoid  (010).  Melanterite  .  .  .41,  43-47 


DESCRIPTIONS    OF    THE    PLATES.  211 

PAGE 

PLATE  V 

Fig.  86.  Monoclinic.  Compound  Form  showing  planes  of 
a  Prism  (110);  two  Hemi-Pyramids  (111,  T21);  a  Clino- 
Dome  (Oil);  two  Hemi-Ortho-Domes  (Poo  or  101,  and 
— P  oo  or  101);  a  Basal  Pinacoid  (001),  and  a  Clino-Pina- 
coid  (010).  Melanterite  -  41,43-47 

Fig.  87.  Orfchorhombic.  Hemimorphic.  Principal  Form  a 
Prism  (210)  with  a  Brachy-Pinacoid  (010).  The  over 
forms  are  two  Macro-Domes  (201,  101),  two  Brachy- 
Domes  (V  or  032,  X  or  012),  and  a  Basal  Pinacoid  (001); 
the  under  form  is  a  Pyramid  (llT).  Calamine,  45,  50, 51,  56,  57 

Fig.  88.  Orthorhombic.  Compound  Form,  easily  mistaken 
for  a  Hemimorphic  crystal,  consisting  of  a  Prism  (110)  and 

a  Brachy-Pinacoid  (010)  and  terminated  at  both  ends  by 

-p 
the  planes  of  a  sphenoid/c<{  111  }•  or  — 

Fig.  89.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Brachy-Dome  (021);  a  Macro-Dome  (101),  and  a 
Basal  Pinacoid  (001).  Niter 50,  51,  57 

Fig.  90.  Orthorhombic.  Compound  Form  showing  the 
planes  of  two  Brachy-Domes  (011,021);  a  Macro-Dome 
(101),  and  a  Basal  Pinacoid  (001).  Niter 50,51,57 

Fig.  91.  Orthorhombic.  Compound  Crystal  showing  the 
planes  of  two  Brachy-Domes  (Oil,  021);  a  Macro-Dome 
(101);  a  Pyramid  (111),  and  a  Basal  Pinacoid  (001). 
Niter ..>.....  ;.......•  .  *  .  .50,51,57 

Fig.  92.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Brachy-Dome  (021);  a  Macro-Dome  (101);  a  Basal 
Pinacoid  (001)  and  a  Pyramid  (111).  Niter  .  .  .  .  50,  51,  57 

Fig.  93.  Orthorhombic.  Compound  Form  showing  the 
Plane  of  a  Brachy-Dome  (Oil);  a  Macro-Dome  (101);  a 
Basal  Pinacoid  (001),  and  a  Prism  (110).  Barite  .  .  50,  51,  57 

Fig.  94.    Orthorhombic.      Compound  Form  showing  the 


212  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

planes  of  a  Prism  (110);  a  Macro-Dome  (101);  a  Brachy- 
Dome  (Oil),  a  Basal  Pinacoid  (001)  and  a  Pyramid  (111). 
Barite 50,51,57 

Fig.  95.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Macro-Dome  (101)  and  a  Brachy-Dome  (Oil).  Bar- 
ite   51,  57 

Fig.  96.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Brachy-Dome  (Oil);  two  Macro-Domes  (101, 301),  and 
a  Pyramid  (111) 51,  57 

Fig.  97.  Orthorhombic.  Compound  Form  showing  planes 
of  two  Prisms  (110, 120),  two  Brachy-Domes  (Oil,  021);  a 
Basal  Pinacoid  (001);  a  Macro-Pinacoid  (100);  a  Brachy- 
Pinacoid  (010);  and  a  Pyramid  (111) 50,51,57 

Fig.  98.  Orthorhombic.  Compound  Form  showing  the 
planes  of  a  Brachy-Dome  (Oil),  and  a  Macro-Dome  (101). 
Stibnite 51,  57 

Fig.  99.  Orthorhombic.  Compound  Form  showing  the 
planes  of  a  Brachy-Dome  (Oil)  and  a  Macro-Dome  (101). 
Calamine 51,  57 

Fig.  100.  Orthorhombic.  Compound  Form  showing  the 
planes  of  a  Brachy  Dome  (Oil);  a  Macro-Dome  (101),  and 
a  Prism  (120).  Barite 51,57 

Fig.  101.  Orthorhombic.  Compound  Form  showing  the 
planes  of  a  Macro-Dome  (101);  a  Brachy-Dome  (Oil);  a 
Prism  (120);  and  a  Brachy  Pinacoid  (010).  Barite  .  50,  51,  57 

Fig.  102.  Orthorhombic.  Compound  Form  showing  the 
planes  of  a  Brachy-Dome  (Oil);  a  Macro-Dome  (101); 
and  a  Basal  Pinacoid  (001).  Barite  .  , 50,51,57 

Fig.  103.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Brachy-Pinacoid  (Oil);  a  Macro-Pinacoid  (101),  and 
a  Basal-Pinacoid  (001).  Barite 50,  51,  57 

Fig.  104.  Orthorhombic.  Compound  Form  showing  the 
planes  of  a  Prism  (110);  a  Macro-Dome  (101),  and  a  Basal 
Pinacoid  (001).  Barite 50,51,57 


DESCRIPTIONS    OF    THE    PLATES.  213 

PAGE 

Fig.  105.   Orthorhombic.    Simple  Form  showing  planes  of 

a  Pyramid  (111).  Sulphur 51,57 

Fig.  106.  Orthorhombic.  Compound  Form  showing  planes 

of  two  Pyramids  (111,  113).  Sulphur 51,57 

Fig.  107.  Orthorhombic.  Simple  Crystal  showing  the 

planes  of  a  Pyramid  (111) 61,57 

Fig.  108.  Orthorhombic.  Compound  Crystal  showing 

planes  of  a  Pyramid  (111)  modified  by  a  Brachy-Pin- 

acoid(OlO) 50,51,67 

Fig.  109.  %  Orthorhombic.  Compound  Form  showing  a 

Pyramid  (111)  modified  by  a  Macro-Pinacoid  (100)  .  50,  51,  57 
Fig.  110.  Orthorhombic.  Compound  Form  showing  planes 

of  a  Pyramid  (111)  modified  by  those  of  a  Brachy-Dome 

(Oil)  .  .  .  .  .  .  .  .  •  •  •  •  •  •  ......-.• 51,57 

Fig.  111.  Orthorhombic.  Compound  Form  showing  planes 

of  a  Pyramid  (111)  and  a  Brachy-Dome  (Oil) 51,  57 

Fig.  112.  Orthorhombic.  Compound  Form  showing  the 

planes  of  a  Pyramid  (111)  and  a  Prism  (110) 51,  57 

PLA.TE  VI 

Fig.  113.   Orthorhombic.    Compound  Form  showing  plane 

of  a  Pyramid  (111)  and  a  Brachy-Dome  (Oil) 51,57 

Fig.  114.  Orthorhombic.  Compound  Form  showing  planes 

of  two  Pyramids  (111,  hkl) ......... 51,57 

Fig.  115.  Orthorhombic.  Compound  Form  showing  planes 

of  a  Pyramid  (111)  and  a  Macro-Dome  (101)  .  .  .    .  .   .51,57 

Fig.  116.  Orthorhombic.  Compound  Form  showing  planes 

of  two  Pyramids  (111,  hkl)  ..   .   ....>..  ......  51,  57 

Fig.  117.  Orthorhombic.  Compound  Form  showing  the 

planes  of  a  Pyramid  (111)  and  a  Prism (210) 61,  57 

Fig.  118.  Orthorhombic.  Compound  Form  showing  planes 

of  a  Pyramid  (111);  a  Prism  (210),  a  Brachy-Dome  (Oil), 

and  a  Brachy-Pinacoid  (010) 50,51,57 


214  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Fig.  119.  Orthorhombic.  Compound  Form  showing  plane 
of  a  Pyramid  (111),  and  a  Brachy-Dome  (021).  Niter  .  .  51,  57 

Fig.  120.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Pyramid  (111);  a  Prism  (110);  a  Brachy-Dome  (021), 
and  a  Brachy-Pinacoid  (010).  Niter .50,51,57 

Fig.  121.  Orthorhombic.  Compound  Form  showing  planes 
of  two  Pyramids  (111,  113);  a  Brachy-Dome  (Oil),  and  a 
Basal-Pinacoid  (001).  Sulphur 50,  51,  57 

Fig.  122.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Pyramid  (111),  and  a  Basal  Pinacoid  (001)  .  . , .  50, 51,  57 

Fig.  123.  Orthorhombic.  Crystal  showing  Prismatic  (110) 
and  Pyramidal  (111)  planes.  Goslarite 51,57 

Fig.  124.  Orthorhombic.  Crystal  showing  Prismatic  (210) 
and  Pyramidal  (111)  planes  . 51,57 

Fig.  125.  Orthorhombic.  Crystal  showing  planes  of  a 
Prism  (110);.  a  Pyramid  (111),  and  a  Brachy-Pinacoid 
(010).  Stibnite 50,51,57 

Fig.  126.  Orthorhombic.  Crystal  showing  planes  of  a 
Prism  (210);  a  Pyramid  (111),  and  a  Brachy-Pinacoid 
(010)  50,51,57 

Fig.  127.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Prism  (110);  a  Pyramid  (111);  a  Brachy-Dome  (Oil), 
and  a  Brachy-Pinacoid  (010).  Goslarite 50,51,57 

Fig.  128.  Orthorhombic.  Compound  Form  showing  planes 
of  two  Prisms  (110, 210)  and  a  Pyramid  (111).  Topaz,  50, 51, 57 

Fig.  129.  Orthorhombic.  Crystal  showing  the  planes  of 
two  Prisms  (110,  210);  a  Pyramid  (111);  a  Brachy-Dome 
(021),  and  a  Basal  Pinacoid  (001).  Topaz 50,  51,  57 

Fig.  130.  Orthorhombic.  Compound  Form  showing  the 
planes  of  a  Pyramid  (111);  a  Macro-Pinacoid  (100),  and  a 
Brachy-Pinacoid  (010) 51 ,  57 

Fig.  131.  Orthorhombic.  Crystal  showing  planes  of  a  Pyra- 
mid (111);  a  Brachy-Pinacoid  (010);  a  Macro-Pinacoid 
(100),  and  a  Brachy-Dome  (Oil) 50,51,57 


DESCRIPTIONS    OF    THE    PLATES.  215 

PAGE 

Fig.  132.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Pyramid  (111);  two  Prisms  (110,  210);  a  Brachy- 
Dome  (Oil);  a  Brachy-Pinacoid  (010),  and  a  Macro-Pina- 
coid(lOO) .  .  .  .50,51,57 

Fig.  133.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Pyramid  (111);  a  Prism  (210),  and  a  Basal  Pinacoid 
(001)  ....;..  ...  .  ••.'.,  '•.-... .  ...  .  >..  r  ,  .50,51,57 

Fig.  134.  Orthorhombic.  Compound  Crystal  showing 
planes  of  two  Pyramids  (111,113);  a  Prism  (110),  and  a 
Brachy-Pinacoid  (010).  .  .  >  .  .  ... .  ......  .50,51,57 

Fig.  135.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Pyramid  (111);  a  Prism  (110);  a  Brachy-Pome  (012); 
a  Macro-Dome  (102),  and  a  Basal  Pinacoid  (001)  .  .  50,  51,  57 

Fig.  136.  Isometric.  Simple  Form.  Positive  Dyakis  Do- 
decahedron (321) 51,135,137,138 

Fig.  137.  Isometric.  Simple  Form.  Negative  Dyakis 
Dodecahedron  (231) 51,135,137,138 

Fig.  138.  Hexagonal.  Simple  Form.  Negative  Rhombo- 
hedron  « •{  OlTl  }>  ............  52,  74,  76,  85,  86, 104 

Fig.  139.  Hexagonal.  Simple  Form.  Positive  Bhombohe- 
dron  «<(  lOll  }• 52,74,78,85,86,  104 

Fig.  140.  Hexagonal.  Simple  Form.  Positive  Scalenohe- 
dron  K]  hkll  }•  or  2131 52,  74,  78,  88-90,  94,  104 

Fig.  141.  Hexagonal.  Simple  Form.  Negative  Scaleno- 
hedron  *<(  ikJil  }•  or  1231  .  .  .  ....  .  52,  74,  78,  89,  90,  94, 104 

Fig.  142.  Orthorhombic.  Simple  Form.  Negative  Sphe- 
noid K]  hhl  \  .  .  .  .  .  .  ...  v  .  .  ...  .  .!.....  55 

Fig.  143.  Orthorhombic.  Simple  Form.  Negative  Sphe- 
noid K.\  hhl  \  .  .  .  .  .  .  '•'*•  ....  V. 55 

Fig.  144.  Orthorhombic.  Simple  Form.  Positive  Sphe- 
noid K\hhl\ - 55 


216  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

PLATE  VII 

Fig.  145.  Orthorhombic.  A  Positive  or  Right-handed 
Sphenoid  «•{  hkl  \  with  an  inscribed  Pyramid  (hkl)  show- 
ing the  method  of  deriving  the  former  from  the  later  55,  56 

Fig.  146.  Orthorhombic.  A  Negative  or  Left-handed 
Sphenoid  K.\  Mel  }•  with  an  inscribed  Pyramid  (hkl)  show- 
ing the  method  of  deriving  the  former  from  the  later  .  55,  56 

Fig.  147.  Orthorhombic.  Simple  Form.  A  Positive  or 
Right-handed  Sphenoid  K.\  tikl\ 55 

Fig.  148.  Orthorhombic.  Simple  Form.  A  Negative  or 
Left-handed  Sphenoid  « \  hkl  }• 55 

Fig.  149.  Orthorhombic.  Compound  Form  showing  a 
Prism  (110),  terminated  by  the  Planes  of  a  Positive  or 
Right-handed  Sphenoid  K]  111  }• .  Epsomite  .  .  .  .  .55,61 

Fig.  150.  Orthorhombic.  Compound  Form  showing  planes 
of  a  Prism  (110)  and  a  Brachy-Pinacoid  (010),  with  the 
ends  of  the  Crystal  terminated  by  the  planes  of  a  Positive 
Sphenoid  «•{  111  }•  and  a  Negative  Sphenoid  K  •{!!!}•. 
Goslarite 55,  61 

Fig.  151.  Tetragonal.  A  Primary  Prism  (110)  terminated 
by  Basal  Pinacoids  (001) 60,61,70 

Fig.  152.  Tetragonal.  Compound  Form  showing  planes  of 
a  Primary  Prism  (110);  a  Secondary  Prism  (100);  and  a 
Basal  Pinacoid  (001) 60,  61,  70 

Fig.  153.  Tetragonal.  Compound  Form  showing  planes  of 
a  Primary  Prism  (110);  a  Secondary  Prism  (100);  a 
Sphenoid  *-j  111  }• ,  and  a  Basal  Pinacoid  (001)  .  .  .60,  61,  70 

Fig.  154.  Tetragonal.  A  Cross-section  showing  the  rela- 
tions of  the  Primary  Prism  (110)  and  the  Primary  Pyra- 
mid (111)  to  the  Lateral  Axes  61,70,73 

Fig.  155.  Tetragonal.  A  Primary  Prism  (110)  terminated 
by  a  Primary  Pyramid  (111) ..  61,  70,  73,74 

Fig.  156.  Tetragonal.    Cross-section   showing  the  relation 


DESCRIPTIONS    OF    THE    PLATES.  217 

PAGE 

of  a  Secondary  Pyramid  (101)  and  a  Secondary  Prism 
(100)  to  a  Primary  Pyramid  (111)  and  a  Primary  Prism 
(110),  and  of  all  to  the  Lateral  Axes 61,  62,  70,  73 

Fig.  157.  Tetragonal.  A  Primary  Pyramid  (111),  termin- 
ating a  Secondary  Prism  (100).  Apophyllite  .  .  61,  70,  73,  74 

Fig.  158.  Tetragonal.  A  Primary  Octahedron  (111)  trun- 
cating the  solid  angles  of  a  Secondary  Prism  (100),  which 
is  terminated  by  a  Basal  Pinacoid  (001).  Apophyllite, 

61,70,73,74 

Fig.  159.  Tetragonal.  A  Primary  Prism  (110)  modified  by 
a  Secondary  Prism  (100)  and  terminated  by  a  Primary 
Pyramid  (111).  Zircon 61,70,73,74 

Fig.  160.  Tetragonal.  A  Cross-section  of  a  Ditetragonal 
Pyramid  (hkl)  and  Ditetragonal  Prism  (frfcO)  showing 
their  relations  to  a  Primary  Prism  (110)  and  to  the 
Lateral  Axes  .. 61,62,70,73 

Fig.  161.  Tetragonal.  A  Ditetragonal  Prism  (fcfcO)  termi- 
nated by  Basal  Pinacoids  (001)  61,70,73,74 

Fig.  162.  Tetragonal.  A  Primary  Pyramid  (111)  with  the 
Axes  drawn  in  .  .  , ".'.  . 60,61,70,73,74 

Fig.  163.  Tetragonal.  A  Secondary  Pyramid  (101)  with  the 
Axes  drawn  in 62,  70,  73,  74 

Fig.  164.  Tetragonal.  A  Primary  Pyramid  (hhl)  with  the 
Axes  drawn  in .'"..' 61,70,73,74 

Fig.  165.  Tetragonal.  A  Secondary  Pyramid  (hOl)  with 
the  Axes  drawn  in  ......  .\  ....  .  .  62,  70,  73,  74 

Fig.  166.  Tetragonal.  A  Primary  Pyramid  (111)  modified 
by  another  Primary  Pyramid  (Mil) 61,  70,  73,  74 

Fig.  167.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
terminal  solid  angles  truncated  by  Basal  Pinacoids  (001), 

61,70,73,74 

Fig.  168.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
lateral  edges  beveled  by  the  planes  of  another  Primary 
Pyramid  (hhl) 61,  70,  73,  74 


218  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Fig.  169.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
lateral  edges  truncated  by  the  planes  of  a  Primary  Prism 
(110) 61,70,73,74 

PLATE    VIII 

Fig.  170.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
terminal  solid  angles  truncated  by  Basal  Pinacoids  (001). 

61,70,73,74 

Fig.  171.  Tetragonal.  Compound  Form  showing  the 
planes  of  two  Primary  Pyramids  (111,  112)  and  a  Basal 
Plane  (001).  Mellite 61,70,73,74 

Fig.  172.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
lateral  solid  angles  truncated  by  a  Secondary  Prism 
(100)  61,70,73,74 

Fig.  173.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
lateral  solid  angles  truncated  by  a  Secondary  Prism  (100), 

61,  70,  73,  74 

Fig.  174.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
lateral  solid  angles  truncated  by  a  Secondary  Prism  (100). 
The  last  three  figures  show  the  change  in  the  appearance 
of  compound  Crystals  made  by  the  enlargement  of  the 
modifying  planes 61,70,73,74 

Fig.  175.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
lateral  solid  angles  replaced  by  the  planes  of  a  Secondary 
Pyramid  (/iOZ) 61,62,70,73,74 

Fig.  176.  Tetragonal.  Compound  Form  showing  planes  of 
two  primary  Pyramids  (111,  113),  and  a  Secondary  Pyra- 
mid (201).  Octahedrite 61,62,70,73,74 

Fig.  177.  Tetragonal.  A  Primary  Pyramid  (111)  modified 
by  a  Secondary  Pyramid  (101) 61,62,70,73,74 

Fig.  178.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
terminal  solid  angles  modified  by  a  Secondary  Pyramid 
(TiOJ) 61,62,70,73,74 


DESCRIPTIONS    OF    THE    PLATES.  219 

PAGE 

Fig.  179.  Tetragonal.  A  Primary  Pyramid  (111)  termin- 
ating a  Primary  Prism,  and  both  modified  by  the  planes 
of  a  Secondary  Pyramid  (hOl) 61,  62,  70,  73,  74 

Fig.  180.  Tetragonal.  Compound  Form  showing  the  planes 
of  a  Primary  Pyramid  (111)  modified  by  the  planes  of  a 
Primary  Pyramid  (112),  a  Secondary  Pyramid  (101),  and 
a  Basal  Pinacoid  (001) ~  ...  61,  62,  70,  73,  74 

Fig.  181.  Tetragonal.  Compound  Form  showing  the  planes 
of  three  Primary  Pyramids  (111,  112,  113);  a  Secondary 
Pyramid  (101);  and  a  Basal  Pinacoid  (001)  .  .  61,  62,  70,  73,  74 

Fig.  182.  Tetragonal.  Compound  Form  showing  the  planes 
of  three  Primary  Pyramids  (111,  112,  113);  a  Secondary 
Pyramid  (101);  a  Secondary  Prism  (100);  and  a  Basal 
Pinacoid  (001) 61,  62,  70,  73,  74 

Fig.  183.  Tetragonal.  Compound  Form  showing  the  planes 
of  two  Primary  Pyramids  (111,112);  a  Secondary  Pyra- 
mid (101);  a  Secondary  Prism  (100);  and  a  Basal  Pina- 
coid (001)  61,70,73,74 

Fig.  184.  Tetragonal.  Simple  Form.  A  Ditetragonal  Pyra- 
mid (fikl).  The  shaded  planes  show  the  planes  sup- 
pressed, while  the  other  planes  are  extended  to  form  a 
Tetragonal  Trapezohedron.  See  page  69  ...  62,  69,  70,  73,  74 

Fig.  185.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
lateral  solid  angles  replaced  by  the  planes  of  a  Ditetra- 
gonal Pyramid  (Ml)  .  .  ,  .  .  .  .  • 61,  62,  70,  73,  74 

Fig.  186.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
terminal  solid  angles  replaced  by  the  planes  of  a  Ditetra- 
gonal Pyramid  (hkl)  ..  . 61,62,70,73,74 

Fig.  187.  Tetragonal.  A  Primary  Pyramid  (111)  with  the 
terminal  edges  beveled  by  the  planes  of  a  Ditetragonal 
Pyramid  (313) 61,  62,  70,  73,  74 

Fig.  188.  Tetragonal.  Compound  Form  showing  the  planes 
of  a  Secondary  Prism  (100);  a  Primary  Pyramid  (111); 
and  a  Ditetragonal  Pyramid  (313).  Zircon  .  61,  62,  70,  73,  74 


220  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Fig.  189.  Tetragonal.  A  Primary  Pyramid  (111)  with  its 
lateral  solid  angles  replaced  by  the  planes  of  a  Ditetra- 
gonal  Prism  (hkO) 61,  70,  73,  74 

Fig.  190.  Tetragonal.  Compound  Form  showing  planes  of 
a  Primary  Pyramid  (111);  a  Primary  Prism  (110);  and  a 
Ditetragonal  Prism  (320).  Cassiterite 61,70,73,74 

Fig.  191.  Tetragonal.  Compound  Form  showing  the 
planes  of  a  Primary  Pyramid  (111);  a  Ditetragonal  Pyra- 
mid (321);  and  a  Primary  Prism  (110).  Cassiterite, 

61,  62,  70,  73,  74 

Fig.  192.  Tetragonal.  Simple  Form.  A  Positive  Sphenoid 
«<{  hhl  j> 66,  67,  69,  70,  73 

Fig.  193.  Tetragonal.  Simple  Form.  A  Negative  Sphen- 
oid M  Mill 66,  67,  69,  70,  73 

Fig.  194.  ,  Tetragonal.  Showing  the  inscribed  Primary 
Pyramid  (Mil)  from  which  the  Positive  Sphenoid  «•{  hhl\ 
is  derived  and  showing  their  mutual  relations, 

66,  67,  69,  70,  73 

Fig.  195.  Tetragonal.  Compound  Form  showing  the 
planes  of  a  Positive  Sphenoid  *  \  hhl  }• ;  a  Negative  Sphen- 
oid K.  \hkl\\  and  two  Secondary  Pyramids  (101,  201). 
Chalcopyrite 66,  67,  70,  73 

Fig.  196.  Tetragonal.  Simple  Form.  A  Positive  Tetra- 
gonal Scalenohedron  *  \  hkl  I 66,67,69,70,73,89 

Fig.  197.  Tetragonal.  Simple  Form.  A  Negative  Tetra- 
gonal Scalenohedron  /c  ]  hkl  [ 66.  67,  69,  70,  73,  89 

Fig.  198.  Tetragonal.  A  Cross  section  showing  the  relation 
of  the  planes  of  the  Tertiary  Pyramid  *  \hkl  \  to  the 
Lateral  Axes  and  to  the  planes  of  the  Primary  Pyramid 
(111)  or  Prism  (110) 40,68,70,73 


DESCRIPTIONS    OF    THE    PLATES.  221 

PAGE 

PLATE   IX 

Fig.  199.  Tetragonal.  Compound  Form  showing  the  planes 
of  a  Primary  Pyramid  (111);  a  Secondary  Pyramid  (201); 
and  a  Tertiary  Pyramid  (421).  Scheelite  .  .  .  .  40,  68,  70,  73 

Fig.  200.  Tetragonal.  Simple  Form.  A  Kight-handed  or 
Positive  Trapezohedron  r\hkl\ 69,  70,  73 

Fig.  201.  Tetragonal.  Simple  Form.  A  Left-handed  or 
Negative  Trapezohedron  r  \hkl\- 69,70,73 

Fig.  202.  Hexagonal.  Section  showing  the  relation  of  the 
Primary  Prism  (10TO)  and  Primary  Pyramid  (loll)  to 
each  other  and  to  the  lateral  axes 74,  76,  81-83,  104 

Fig.  203.  Hexagonal.  Simple  Form.  A  Primary  Pyramid 
(lOll) 74,  76,  81-83,  104 

Fig.  204.  Hexagonal.  Simple  Form.  A  Secondary  Pyra- 
mid (1122) 74,  76,  81-83,  104 

Fig.  205.  Hexagonal.  A  Primary  Prism  (IQlO)  terminated 
by  Basal  Pinacoids  (0001) 74,76,80-83,104 

Fig.  206.  Hexagonal.  A  Secondary  Prism  (1120)  termi- 
nated by  Basal  Pinacoids  (0001) 74,  76,  80-83, 104 

Fig.  207.  Hexagonal.  A  Dihexagonal  Prism  (/tHO)  or 
(2130)  terminated  by  Basal  Pinacoids  (0001)  .  74,  76,  80,  81, 104 

Fig.  208.  Hexagonal.  Simple  Form.  A  Dihexagonal 
Pyramid  (hkil) 74,  76,  82,  104 

Fig.  209.  Hexagonal.  A  Diagram  to  demonstrate  the  rela- 
tion of  the  parameters  of  Secondary  Prisms  and  Pyramids 
to  those  of  the  corresponding  Primary  forms.  See  pages 
83,  84  .......  /'.  ,  .->_  .  i  ......  74,  76,  82-84,  104 

Fig.  210.  Hexagonal.  Simple  Form.  A  Positive  or  Bight- 
handed  Trapezohedron  T  \  hkll  ^ 74,  76,  94,  95, 104 

Fig.  211.  Hexagonal.  Simple  Form.  A  Negative  or  Left- 
handed  Trapezohedron  T  <[  ikld  \' 74,  76,  94,  95, 104 

Fig.  212.  Hexagonal.  A  Cross  Section  showing  the  position 
of  the  planes  of  a  Secondary  Prism  (1120)  or  Pyramid 


222  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

(lf22)  relative  to  a  Primary  Prism  (loTO)  or  Pyramid 
(lOll)  and  to  the  Lateral  Axes 74,  76,  81-83, 104 

Fig  213.  Hexagonal.  A  Cross  Section  showing  the  rela- 
tive position  of  the  planes  of  a  Tertiary  Prism  IT  •(  /iHO  }• 
or  Pyramid  *  \  hkil  \  to  the  planes  of  a  Primary  Prism 
(10TO)  or  Pyramid  (lOTl)  and  to  the  Lateral  Axes, 

74,76,81,91-93,104 

Fig.  214.  Hexagonal.  Hemimorphic  Form.  lodyrite  Type 
showing  the  planes  of  an  over  Hemi-Pyramid  (1011);  a 
Prism  (10TO),  and  a  Basal  Pinacoid  (0001)  .  74,  76,  81, 102,  104 

Fig.  215.  Hexagonal.  Hemimorphic  Form.  lodyrite  Type 
showing  the  planes  of  a  Secondary  Prism  (1120);  the  over 
planes  of  a  Primary  Pyramid  (4041 )  and  Basal  Pinacoid 
(0001),  and  the  under  planes  of  a  Primary  Pyramid  (4045) 
and  a  Dihexagonal  Pyramid  (9-9-18-  20).  lodyrite, 

74,  76,  80,  81,  102,  104 

Fig.  216.  Hexagonal.  Hemimorphic  Form.  lodyrite  Type 
showing  the  planes  of  a  Secondary  Prism  (1120);  the  over 
planes  of  a  Primary  Pyramid  (4041)  and  a  Basal  Pinacoid 
(0001),  and  the  under  planes  of  a  Primary  Pyramid  (4045). 
lodyrite 74,  76,80,81,102,104 

Fig.  217.  Hexagonal.  Hemimorphic  Form.  Nephelite 
Type  showing  the  planes  of  a  Primary  Prism  (10TO);  the 
over  planes  of  a  Primary  Pyramid  (1011),  and  the  under 
planes  of  another  Primary  Prism  (20~21)  .  .  74,  76,  81, 103, 104 

Fig.  218.  Hexagonal.  A  Primary  Pyramid  (loll)  with  the 
alternate  planes  shaded.  If  the  shaded  planes  are  sup- 
pressed and  the  others  are  extended  until  they  meet  a 
Rhombohedron  K-{  loll  }•  will  be  produced.  See  page  85, 

74,  76,81,83,85,104 

Fig.  219.  Hexagonal.  A  Cross-section  of  a  Dihexagonal 
Prism  (ftfctO)  and  Pyramid  (hkil)  to  the  Primary 
Prism  (lOlO)  and  Pyramid  (loll)  respectively,  and  to  the 
Lateral  Axes 74,76,81,82,91,99,104 


DESCRIPTIONS    OF    THE    PLATES.  223 

PAGE 

Fig.  220.  Hexagonal.  A  Secondary  Prism  (1120)  termin- 
ated by  Basal  Pinacoids  (0001).  The  alternate  planes  are 
shaded.  If  the  shaded  planes  are  suppressed  and  the  non- 
shaded  ones  extended  a  Secondary  Trigonal  Prism  will 
result  KT^  1120  }• .  See  Figure  221  and  page  99, 

74,  76,80,  81,99,  104 

PLATE  X 

Fig.  221.  Hexagonal.  A  Secondary  Trigonal  Prism 
KT\  1120  }•  terminated  by  Basal  Pinacoids  (0001), 

74,  76,  80,  99,  104 

Fig.  222.  Hexagonal.  A  simple  form.  A  Negative  Blwm- 
bohedron  «•(  0221  j> 74,  76,  87, 104 

Fig.  223.  Hexagonal.  A  simple  form.  A  Negative  Rhom- 
bohedron  — $A*  or  «-{  0112  }• 74,76,85,87,104 

Fig.  224.  Hexagonal.  Compound  Form,  showing  the  planes 
of  two  Positive  Primary  Rhoinbohedrons  /c-j  1011  }• , 
K-J1012}-,  and  a  Negative  Primary  Rhombohedron 
H  OlTl  }•  .  .  . 74,  76,  87,  104 

Fig.  225.  Hexagonal.  Compound  Form  showing  the  planes 
of  a  Positive  Primary  Rhombohedron  «•{  1011  }•  and  two 
Negative  Primary  Rhombohedrons  «•{  0221  }•;«•{  0112  }• » 

74,  76,  87,  88,  104 

Fig.  226.  Hexagonal.  Compound  Form  showing  the  planes 
of  a  Positive  Primary  Rhombohedron  «•{  1011  }•  and  a 
Negative  Primary  Rhombohedron  «•{  OlTl  j-  .  .  74,76,  87, 104 

Fig.  227.  Hexagonal.  A  Positive  Rhombohedron  K-{  4041  }• 
terminated  by  a  Positive  Rhombohedron  «•{  1011  }-.  Cal- 
cite *  .  .-.  ,\.  ....  ....  -  .  .74,76,87,104 

Fig.  228.  Hexagonal.  A  Negative  Rhombohedron  K-{  0221  }• 
with  its  vertical  edges  truncated  by  a  Positive  Rhombo- 
hedron K-jloTl}-.  Calcite 74,76,87,88,104 


224  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Tig.  229.  Hexagonal.  Holohedral.  A  Simple  Form.  A 
Dihexagonal  Pyramid  (hkil)  with  its  alternative  pairs 
of  planes  shaded  to  show  the  planes  extended  to  form  the 
Scalenohedron  K-{  hkil  }•  the  non-shaded  planes  are  sup- 
pressed. See  page  88 74,  76,  82,  88, 104 

Fig.  230.  Hexagonal.  Showing  a  Cross-section  of  a  Scaleno- 
hedron ««{  hkil  }- 74,  76,  89,  99,  104 

Fig.  231.  Hexagonal.  Figure  showing  the  relation  of  the 
Bhombohedron  K-{  1011  J>  of  the  Middle  Edges  to  a  Scaleno- 
hedron K  <{  2131  }• 74,  76,  89,  90,  104 

Fig.  232.  Hexagonal.  A  Dihexagonal  Pyramid  (hkil) 
with  an  inscribed  Scalenohedron  K-{  hkil  }•  .  74,  76,  88,  89,  104 

Fig.  233.  Hexagonal.  Showing  the  relation  of  a  Primary 
Pyramid  (1011)  to  a  Primary  Rhombohedron  «-{  loll  }•, 

74,  76, 104 

Fig.  234.  Hexagonal.  A  Simple  Form.  The  Dihexagonal 
Pyramid  (hkil)  with  the  alternate  planes  above  and  the 
planes  below,  joining  them  base  to  base,  shaded.  If  the 
sets  of  the  shaded  or  of  the  non-shaded  planes  are  ex- 
tended a  Tertiary  Pyramid  n\  hkil  }•  can  be  formed.  See 
page  92 74,  76,  82,  92,  104 

Fig.  235.  Orthorhombic.  Simple  Form.  Pyramid  (111) 
with  its  alternate  planes  shaded.  If  either  set  of  alter- 
nate planes  is  extended  and  the  other  set  suppressed  a 
Sphenoid  «-{  111  [-  will  be  formed 55,56 

Fig.  236.  Tetragonal.  Simple  Form.  A  Primary  Pyramid 
(111)  with  its  alternate  faces  shaded.  If  either  set  of 
shaded  or  non-shaded  faces  are  suppressed  and  the  other 
set  extended,  a  Sphenoid  will  be  formed  K-{  ill  }•  .  .  .  65,  66 

Fig.  237.  Tetragonal.  A  Simple  Form.  A  Ditetragonal 
Pyramid  (hkl)  with  its  alternate  pairs  of  planes  shaded. 
If  the  four  alternate  pairs  of  shaded  planes  or  of  the  non- 
shaded  planes  are  suppressed  and  the  other  alternate  pairs 


DESCRIPTIONS    OF    THE    PLATES.  225 

PAGE 

of  planes  extended,  a  Tetragonal  Scalenohedron  « •{  kkl  }• 
will  be  formed 66 

Fig.  238.  Tetragonal.  Compound  Form.  A  Ditetragonal 
Prism  (hkQ)  terminated  by  Basal  Pinacoids  (0001).  Each 
alternate  plane  of  the  Prism  is  shaded.  If  the  shaded 
planes  are  suppressed  and  the  others  extended,  the  result- 
ing form  is  a  Tertiary  Prism  *  \  hkQ  }• 67 

Fig.  239.  Tetragonal.  Simple  Form.  A  Ditetragonal 
Pyramid  (hkl).  If  the  alternate  or  shaded  planes  above 
and  the  alternate  or  shaded  planes  immediately  below  (or 
base  to  base)  are  considered  suppressed  and  the  other 
planes  are  considered  extended,  the  resultant  form  is  a 
Tertiary  Pyramid  ir\hkl\ 67,68 

Fig.  240.  Tetragonal.  Compound  Form  showing  planes  of 
three  Primary  Pyramids  (111,221,441);  of  two  Second- 
ary Pyramids  (101,201);  of  four  Ditetragonal  Pyramids 
(121,  421,  132,  411);  of  a  Primary  Prism  (110);  of  a 
Secondary  Prism  (100);  of  a  Ditetragonal  Prism  (210), 
and  a  Basal  Pinacoid  (001).  Vesuvianite  .  * 69,  74 

Fig.  241.  Hexagonal.  A  Simple  Form.  A  Dihexagonal 
Pyramid  (hktl).  The  alternate  upper  and  lower  planes 
are  shaded.  If  these  shaded  planes  are  suppressed  and 
the  others  are  extended,  a  Trapezohedron  r\  hkil  }•  will 
be  formed.  See  pages  93,  94 74,  76,  82,  93, 104 

Fig.  242.  Hexagonal.  A  Dihexagonal  Prism  (hklO)  ter- 
minated by  Basal  Pinacoids  (0001).  The  alternate  planes 
of  the  Prism  are  shaded.  If  the  shaded  or  non-shaded 
planes  are  suppressed  and  the  other  alternate  set  of 
planes  are  extended,  the  result  produced  will  be  a  Ter- 
tiary Prism  TT  1  hkiQ  }• .  See  pages  91 , 92  .  .  74, 76, 80, 81 , 91 , 104 

Fig.  243.  Hexagonal.  Simple  Form.  A  Secondary  Pyra- 
mid (h'h'Zh'l)  with  the  axes  drawn  in.  The  alternate 
upper  and  lower  faces  of  this  Pyramid  are  shaded.  If  the 


226  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

shaded  or  non-shaded  planes  are  suppressed  and  the  others 
extended  a  Secondary  Rhombohedron,  ™-{  h'  h'  2h'  I  }•  will 
be  the  resulting  form.  See  pages  96,  97.  74,  76,  82,  83,  96, 104 

Fig.  244.  Hexagonal.  Simple  Form.  A  Scalenohedron 
K]  Jikil  \  with  its  axes  drawn  in.  The  alternate  lower 

'  and  upper  planes  of  the  Scalenohedron  are  shaded.  If 
either  the  shaded  or  non-shaded  planes  are  suppressed  and 
the  other  planes  extended  a  Tertiary  Rhombohedron 
TT/C-J  hkil  }>  will  be  produced.  See  pages  97,  98, 

74,  76,  82,  96,  104 

Fig.  245.  Hexagonal.  A  Scalenohedron  «•{  fikll  }•  similar 
to  Fig.  244,  but  the  other  planes  are  shaded.  See  pages 
97,  98 74,  76,  89,  97,  104 

PLATE    XI 

Fig.  246,  Hexagonal.  Compound  Form  showing  planes  of 
a  Dihexagonal  Prism  (/iJBO)  and  of  a  Basal  Pinacoid 
(0001).  The  alternate  pairs  of  planes  are  shaded.  If  these 
or  the  non- shaded  pairs  of  planes  are  suppressed  and  the 
other  pairs  of  planes  extended,  the  form  produced  will  be 
the  Ditrigonal  Prism  KT  ]  hklQ  }• .  See  page  99, 

74,  76,80,  81,99,  104 

Fig.  247.  Hexagonal.  Simple  Form.  A  Negative  or  Left- 
handed  Ditrigonal  Prism  KT^  ikhO  }>  terminated  by  Basal 
Pinacoids  (0001)  .  . 74,76,80,99,104 

Fig.  248.  Hexagonal.  Simple  Form.  A  Positive  or  Right- 
handed  Ditetragonal  Prism  KT^  hkiQ  }-  terminated  by 
Basal  Pinacoids  (OC01) 74,  76,  80,  99,  104 

Fig.  249.  Hexagonal.  Simple  Form.  A  Secondary  Pyra- 
mid (h'  h'  2/i •  I).  The  alternate  planes  above  and  the 
planes  below,  whose  bases  are  coincident,  are  shaded.  If 
these  shaded  planes  are  suppressed  and  the  other  planes 
are  extended,  the  result  forms  a  Secondary  Trigonal 
Pyramid  «r  ^  h'h'Vh'l  \ .  See  pages  99, 100  .  74, 76,  82, 83, 100, 104 


DESCRIPTIONS    OF    THE    PLATES.  227 

PAGE 

Fig.  250.  Hexagonal.  Simple  Form.  A  Positive  or  Eight- 
handed  Secondary  Trigonal  Pyramid  KT  \  h~  li-  2k- 1  }> .  See 
pages  99,  100 74,  76, 100,  104 

Fig.  251.  Hexagonal.  Simple  Form.  A  Negative  or  Left- 
handed  Secondary  Trigonal  Pyramid  KT  •{  2h'  /F/FZ  }• .  See 
pages  99,  100 74,  76,  100, 104 

Fig.  252.  Hexagonal.  Simple  Form.  Negative  Scalenohe- 
dron  K  -{  ikhl  }•  with  the  alternate  upper  and  lower  planes 
joined  base  to  base,  shaded.  If  the  shaded  planes  are 
suppressed  and  the  non-shaded  ones  extended,  or  vice  versa 
a  Negative  Bight  or  Left-handed  Trigonal  Trapezohedron 
is  produced  KT -{  Mhl  }• .  See  page  100  .  74,  76,  89, 90,  94, 100, 104 

Fig.  253.  Hexagonal.  Simple  Form.  A  Positive  Scaleno- 
hedron  « •{  2131  }-  with  the  alternate  upper  and  lower  planes, 
joined  base  to  base,  shaded.  If  the  shaded  planes  are 
suppressed  and  the  non-shaded  ones  extended,  or  vice 
versa  a  Positive  Right-  or  Left-handed  Trigonal  Trapezo- 
hedron K.T  \  2131  }•  is  formed.  See  page  100, 

74,  76,  89,  90,  94,  100,  104 

Fig.  254.  Hexagonal.  A  Compound  Form  showing  the 
planes  of  a  Primary  Prism  (loTo)  terminated  by  the  planes 
of  a  Primary  Pyramid  (lOfl).  Quartz  .  .  .  74,  76,  81,  83, 104 

Fig.  255.  Hexagonal.  Compound  Form  showing  planes  of 
a  Primary  Prism  (1010),  of  a  Primary  Pyramid  (1011), 
and  of  a  Dihexagonal  Pyramid  (h-  lv  2&-  I)  .  74,  76,  81,  83, 104 

Fig.  256.  Hexagonal.  Compound  Form,  showing  the 
planes  of  a  Primary  Pyramid  (1011)  with  its  solid  lateral 
angles  truncated  by  the  planes  of  a  Secondary  Prism 
(1120) 74,76,81,83,104 

Fig.  257.  Hexagonal.  Compound  Form  showing  the  planes 
of  a  Primary  Pyramid  ( lOTl )  with  its  lateral  solid  angles 
replaced  by  the  planes  of  a  Dihexagonal  Prism  (ABO), 

74,86,81,83,104 


228  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Fig.  258.  Hexagonal.  Compound  Form  showing  the  planes 
of  a  Primary  Pyramid  (loll)  with  its  lateral  solid  angles 
replaced  by  the  planes  of  a  Secondary  Pyramid  (1122), 

74,  76,  81,  83, 104 

Fig.  259.  Hexagonal.  Compound  Form  showing  the  planes 
of  a  Primary  Pyramid  (loll)  with  its  lateral  solid  angles 
replaced  by  the  planes  of  a  Dihexagonal  Pyramid  (hM), 

74,76,  81-83,104 

Fig.  260.  Hexagonal.  Compound  Form  showing  the  planes 
of  a  Primary  Pyramid  (loTl)  with  its  lateral  edges  beveled 
by  a  second  Primary  Pyramid  (htihl) .  .  .  .74,  76,  81,  83, 104 

Fig.  261.  Hexagonal.  Compound  Form  showing  the  planes 
of  a  Primary  Pyramid  (loTl)  with  its  vertical  edges  trun- 
cated by  the  planes  of  a  Secondary  Pyramid  (1122), 

74,  76,  81-83,  104 

Fig.  262.  Hexagonal.  Compound  Form  showing  a  Primary 
Pyramid  (loTl)  with  its  vertical  edges  beveled  by  the  planes 
of  a  Dihexagonal  Pyramid  (2133) 74,  76,  81-83, 104 

Fig.  263.  Hexagonal.  Compound  Form  composed  of  a 
Primary  Pyramid  (1011)  with  its  vertical  solid  angles 
truncated  by  Basal  Planes  (0001)  .  .  .  .74,76,80,81,83,104 

Fig.  264.  Hexagonal.  A  Primary  Pyramid  (loTl)  with  its 
vertical  solid  angles  replaced  by  a  second  Primary  Pyra- 
mid (hOhl) 74,76,81,83,104 

Fig.  265.  Hexagonal.  A  Primary  Pyramid  (loll)  with  its 
vertical  solid  angles  replaced  by  a  Secondary  Pyramid 
(1122) 74,  76,  81,  83,  104 

Fig.  266.  Hexagonal.    A  Primary  Pyramid  (loll)  with  its 
-vertical  solid  angles  replaced  by  the  planes  of  a  Dihexa- 
gonal Pyramid  (2133) 74,  76,  81-83,  104 

Fig.  267.  Hexagonal.  A  Secondary  Pyramid  (1122)  with  its 
vertical  solid  angles  replaced  by  the  planes  of  a  Primary 
Bhombohedron  K  -{  hOhl  }- 74,  76,  82,  83,  104 


DESCRIPTIONS    OF   THE    PLATES.  229 

PAGE 

Fig.  268.  Hexagonal.  Compound  Form  composed  of  a  Posi- 
tive Rhombohedron  K  \  lofl  }>  joined  to  a  Negative  Rhom-  ' 
bohedron   « ^  oiTl  \ .    United  they  form  a  Primary  Pyra- 
mid (lOll)  .   .  .  .  \ .  i   .   .74,76,83,104 

Fig.  269.  Hexagonal.  A  Primary  Rhombohedron  *•{  1011  }• 
with  its  vertical  solid  angles  truncated  by  a  Basal  Pina- 
coid  (0001) .74,76,80,104 

PLATE  XII 

Fig.  270.  Hexagonal.  A  Positive  Rhombohedron  K-{  2021  }- 
with  its  vertical  solid  angles  replaced  by  the  planes  of 
another  Positive  Rhombohedron  « {  0332  J-  ...  74,  76,  87, 104 

Fig.  271.  Hexagonal.  A  Positive  Rhombohedron  «•{  2021  }- 
with  its  vertical  solid  angles  replaced  by  the  planes  of  a 
Negative  Rhombohedron  *-{  Qhhl  }• 74,  76,  87, 104 

Fig.  272.  Hexagonal.  A  Positive  Rhombohedrpn  «-{  idll  }• 
with  its  vertical  solid  angles  replaced  by  Basal  Planes 
(0001) 74,  76,  87,  104 

Fig.  273.  Hexagonal.  A  Positive  Rhombohedron  «•{  10U  }• 
with  its  lateral  solid  angles  replaced  by  the  planes  of  a 
Scalenohedron  *•{  hkil  \ • .  .  .  .  .  .  74,  76, 104 

Fig.  274.  Hexagonal.  A  Positive  Rhombohedron  «-{  lOll  }- 
with  its  lateral  solid  angles  replaced  by  the  planes  of  a 
Negative  Rhombohedron  « -{  Qhhl  }•  .......  .74,76,104 

Fig.  275.  Hexagonal.  A  Positive  Rhombohedron  « •{  loll  }- 
with  its  solid  lateral  angles  replaced  by  the  planes  of  a 
Negative  Rhombohedron  K  -(  0221  }•  and  its  terminal  solid 
angles  truncated  by  Basal  Pinacoids  (0001)  .  74,  76,  80,  87,  104 

Fig.  276.  Hexagonal.  A  Positive  Rhombohedron  «•{  hQhl  }• 
modified  by  the  planes  of  a  Secondary  Pyramid 
*\h'h-2h'l\ 74,76,82,87,104 

Fig.  277.  Hexagonal.  A  Positive  Rhombohedron  *\  1011  }• 
modified  by  the  planes  of  a  Secondary  Pyramid  K\  2243  }• , 


230  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

and  those  of  a  Positive  Rhombohedron  « -{  10U  }• .    Hema- 
tite   74,76,87,104 

Fig.  278.  Hexagonal.  A  Secondary  Prism  (1120)  termin- 
ated by  the  planes  of  a  Secondary  Rhombohedron  K  -\  0221  }• . 
Dioptase 74,76^81,104 

Fig.  279.  Hexagonal.  A  Positive  Rhombohedron  «•{  1011  }• 
with  its  lateral  edges  truncated  by  a  Secondary  Hexa- 
gonal Prism  (1120) 74,76,81,104 

Fig.  280.  Hexagonal.  A  Positive  Rhombohedron  « •{  1011  }- 
with  its  lateral  solid  angles  replaced  by  the  planes  of  a 
Negative  Rhombohedron  «•{  Olll  }• ,  and  its  lateral  edges 
by  the  planes  of  a  Secondary  Prism  (1120)  .  74,  76,  8K,  87,  104 

Fig.  281.  Hexagonal.  A  Positive  Rhombohedron  «•{  20~21  J- 
with  its  terminal  solid  angles  replaced  by  the  planes  of  a 
Scalenohedron /<*!  hk\l\ 74,76,104 

Fig.  282.  Hexagonal.  A  Positive  Rhombohedron 
«.\  16-  0-  16- 1  \  with  its  terminal  solid  angles  replaced 
by  the  planes  of  a  Negative  Rhombohedron  K.\  0112  \. 
Calcite 74,  76, 104 

Fig.  283.  Hexagonal.  A  Primary  Prism  (10TO)  termin- 
ated by  the  planes  of  a  Negative  Rhombohedron  *\  0112  \. 
Calcite 74,76,81,104 

Fig.  284.  Hexagonal.  Hemimorphic  Form  showing  planes 
of  a  Primary  Trigonal  Prism  KT\  1010  \  and  a  Secondary 
Prism  (1120).  It  is  terminated  at  the  over  end  by  a  Posi- 
tive Primary  Rhombohedron  K-{  1011  }-,and  a  Negative 
Primary  Rhombohedron  « •{  OH2  }•  which  truncates  the 
edges  of  the  Positive  Rhombohedron.  The  under  end  is 
formed  by  a  Positive  Primary  Rhombohedron  « •{  1011  }• , 
and  a  Negative  Rhombohedron  « -j  0221  j- .  Tourmaline, 

74,  76,  104 

Fig .  285.  Hexagonal.  A  Positive  Rhombohedron  K  •{  2021  }• 
with  its  vertical  or  terminal  edges  beveled  by  the  planes 
of  a  Scalenohedron  K  \h~kil\- 74,76,104 


DESCRIPTIONS    OF    THE    PLATES.  231 

PAGE 

Fig.  286.  Hexagonal.  .A  Compound  Form  showing  the 
planes  of  a  Positive  Rhombohedron  «-j  1011  }•  and  of  a 
Negative  Rhombohedron  K\  0112  }• .  Calcite  .  .  74,  76,  87, 104 

Fig.  287.  Hexagonal.  A  Scalenohedron  «•{  2131  \  with  its 
lateral  angles  replaced  by  the  planes  of  a  Primary  Pyra- 
mid (4041) 74,  76,  89,  104 

Fig.  288.  Hexagonal.  A  Scalenohedron  n\  2131  }•  with  its 
lateral  solid  angles  replaced  by  the  planes  of  a  Dihexa- 
gonal  Pyramid  (hkil)  .  .  .  . 74,76,89,104 

Fig.  289.  Hexagonal.  A  Scalenohedron  « \  2131  \  with  its 
terminal  solid  angles  truncated  by  Basal  Pinacoids 
(0001) 74,76,81,89,104 

Fig.  290.  Hexagonal.  A  Scalenohedron  K \  2131  \  with  its 
terminal  solid  angles  replaced  by  another  Scalenohedron 
K-J2134}- 74,76,89,104 

Fig.  291.  Hexagonal.  A  Scalenohedron  K\  2131  \  with  its 
terminal  solid  angles  replaced  by  a  Positive  Rhombohe- 
dron  K\  20"21  \ 74,  76,  89, 104 

Fig.  292.  Hexagonal.  A  Scalenohedron  K  \  2131  \-  with  its 
terminal  solid  angles  replaced  by  another  Scalenohedron 
*\  4153  }- 74,  76,89,  104 

Fig.  293.  Hexagonal.  A  Scalenohedron  «-{  2131  }•  with  its 
alternate  terminal  edges  truncated  by  the  planes  of  a 
Ehombohedron  ««{  15-  5-  20-  4  }• 74,  76,  89, 104 

Fig.  294.  Hexagonal.  A  Scalenohedron  « •{  2131  }•  with  its 
alternate  terminal  edges  truncated  by  a  Negative  Rhom- 
bohedron ^0221  }• 74,76,89,104 

Fig.  295.  Hexagonal.  A  Scalenohedron  «<{  2131  }>  with  its 
lateral  zigzag  edges  beveled  by  the  planes  of  another 
Scalenohedron  K  \  11- 1-  12- 10  }• 74,  76,  89, 104 

Fig.  296.  Hexagonal.  A  Scalenohedron  «•{  2131  }•  with  its 
alternate  vertical  edges  beveled  by  the  planes  of  a  second 
Scalenohedron  « <{  6lT4  }- 74,  76,  89,  104 


232  DESCRIPTIONS   OF    THE    PLATES. 

PAGB 

Fig.  297.  Hexagonal.  A  Scalenohedron  ««{  2131  }•  with  its 
alternate  vertical  edges  beveled  by  the  planes  of  a  second 
Scalenohedron  « <{  8-  4-  12-  5  j- 74,  76,  89, 104 

PLATE   XIII 

Fig.  298.  Hexagonal.  A  Scalenohedron  * •{  2131  }•  with  its 
lateral  edges  truncated  by  a  Secondary  Prism  (1120). 
Calcite 74,76,81,89,104 

Fig.  299.  Hexagonal.  A  Scalenohedron  «•{  2131  }•  with  its 
lateral  edges  truncated  by  a  Secondary  Prism  (1120). 
This  form  shows  a  greater  development  of  the  prismatic 
planes  than  does  Fig.  298.  Calcite  .  .  74,  76,  81^89, 104 

Fig.  300.  Hexagonal.  A  Positive  Scalenohedron  *\  2131  }• 
with  its  lateral  solid  angles  replaced  by  another  Positive 
Scalenohedron  «-{  4041  }-.  Calcite 74,  76,  89, 104 

Fig.  301.  Hexagonal.  A  Positive  Scalenohedron  *-{  2131  }• 
with  its  terminal  solid  angles  replaced  by  a  Positive 
Rhombohedron  «-{  loll  }-.  Calcite 74,76^,89,104 

Fig.  302.  Hexagonal.  A  Positive  Scalenohedron  «•{  2131  }• 
with  its  lateral  solid  angles  replaced  by  a  Primary  Prism 
( 1010)  and  with  its  terminal  solid  angles  replaced  by  the 
planes  of  a  Positive  Scalenohedron  « -j  2134  }• .  Calcite, 

74,  76,  81,  89, 104 

Fig.  303.  Hexagonal.  A  Positive  Scalenohedron  «<{  2131  }• 
with  its  alternate  vertical  edges  truncated  by  the  planes 
of  a  Negative  Rhombohedron  *•{  0221  }• ,  its  lateral  solid 
angles  replaced  by  the  planes  of  a  Primary  Prism  (1010) 
and  its  terminal  solid  angles  replaced  by  the  planes  of  a 
Positive  Rhombohedron  K-{  1011  }• .  Calcite,  74,  76,  81,  89, 104 

Fig.  804.  Hexagonal.  Compound  Form  showing  the  planes 
of  two  Positive  Scalenohedrons  K  -{  2131  }•  and  K  •{  3251  }• ; 
of  two  Positive  Rhombohedrons  K  ^  1010  1-  and  « ^  4041  }• , 
and  a  Primary  Prism  (lOlO).  Calcite  .  .  .74,76,81,89,104 


DESCRIPTIONS    OF    THE    PLATES.  233 

PAGE 

Fig.  305.  Hexagonal.  Compound  Form  showing  the  planes 
of  a  Negative  Scalenohedron  /c-{  1341}*;  of  a  Positive 
Scalenohedron  +  #3  or  K-{  2131  }• ,  with  its  ends  terminated 
by  the  planes  of  a  Positive  Rhombohedron  *•{  lOfl  }- ;  and 
of  a  Negative  Rhombohedron  «•<{  0221  [-.  Calcite, 

74,  76,  89,  104 

Fig.  306.  Hexagonal.  A  Secondary  Pyramid  (1122)  with 
its  lateral  solid  angles  replaced  by  the  planes  of  a  Positive 
Rhombohedron  «-{  0332  }• 74,76,82,104 

Fig.  307.  Hexagonal.  A  Primary  Prism  (loTo)  terminated 
by  the  planes  of  a  Positive  Rhombohedron  K-{  loll  }•  and  a 
Negative  Rhombohedron  *-j  OlTl  }-  ...  74,  76,  81-83,  87, 104 

Fig.  308.  Hexagonal.  A  Primary  Prism  (loTo)  terminated 
by  a  Positive  Rhombohedron  K-{  loll  }•  and  a  Negative 
Rhombohedron  K  -{  OlTl  }- ,  and  its  lateral  solid  angles  re- 
placed by  the  planes  of  a  Secondary  Pyramid  (1121). 
Quartz ...  .74,76,81,83,100,104 

Fig.' 309.  Hexagonal.  A  Compound  Form  showing  the 
planes  of  a  Primary  Prism  (1010);  of  a  Positive  and  a 
Negative  Rhombohedron  « -J  loTl  }-,*-{  OlFl  }• ;  and  of  two 
Trigonal  Trapezohedrons  KT-{  5161  }-  and  «•-{  1121  }-. 
Quartz 74,76,81,83,87,100,104 

Fig.  310.  Hexagonal.  Compound  Form  showing  the 
planes  of  a  Primary  Prism  (1010);  of  two  Positive  Rhom- 
bohedrons  «-{  loll  }-  and  «-{  3031  }- ;  of  a  Negative  Rhom- 
bohedron K  \  0111  }-,  and  two  Trigonal  Trapezohedrons 
KT\  5l"61  \ ,  and  KT\  1121  }• .  Quartz,  74,  76,  81,  83,  87, 100, 104 

Fig.  311.  Hexagonal.  Compound  Form  showing  the 
planes  of  Primary  Prism  (1010);  of  a  Positive  Rhombo- 
hedron K-{  1011  }•;  of  a  Negative  Rhombohedron  «-{  0111  }•; 
and  of  two  Trigonal  Trapezohedrons  KT-{  1121  }-  and 
Kr-15161}-.  Quartz 74,76,81,83,87,100,104 

Fig.  312.  Hexagonal.  Compound  Form  showing  the  planes 
of  a  Primary  Prism  (1010);  of  two  Positive  Rhombo- 


234  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

hedrons  «•{  lofl  }-,«:-{  5051  }• ;  of  a  Negative  Ilhombohedron 
K-jOlTl}-;  two  Trigonal  Trapezohedrons  KT-{  1121  }-, 
*r-{516U.  Quartz .  .  .74,76,81,83,87,100,104 

Fig.  313.  Hexagonal.  A  Compound  Form  showing  the 
planes  of  a  Primary  Prism  (  oo  p  or  1010);  of  two  Rhom- 
bohedrons  R  or  K\  loll  }-,  4  E  or  *•{  4041  }-  and  two 
Scalenohedrons  Ez  or  «•{  2131  }-  and  J?5  or  «•{  3251  }-. 
Caleite 74,  76,  81,  83,  104 

Fig.  314.  Hexagonal.  Compound  Form  showing  planes  of 
a  Primary  Prism  (1010);  of  a  Positive  Rhombohedron  E 
or  «•{  1011  }•;  of  three  Negative  Rhombohedrons  -\  E  or 
K-{  OlT2  }- ,  -4/5  J?  or  «•{  0445  }- ,  -2  J?  or  «-{  0221  }- ,  and  of 
two  Scalenohedrons  /£3  or  «-{  2131  }-,  i  J?3  or  /c^{  2134  }-. 
Caleite 74,  76,81,83,87,104 

Fig.  315.  Hexagonal.  A  Primary  Pyramid  (loll)  with  its 
vertical  or  terminal  solid  angles  truncated  by  Basal  Pina- 
coids  (0001).  Apatite 74,76,80,81,83,104 

Fig.  316.  Hexagonal.  Compound  Form  showing  planes  of 
a  Primary  Prism  (1010);  of  a  Primary  Pyramid  (loll); 
and  of  a  Basal  Pinacoid  (0001).  Apatite. 

74,76,80,81,83,104 

Fig.  317.  Hexagonal.  Compound  Form  showing  planes  of 
a  Primary  Prism  (lOlb);  of  a  Secondary  Pyramid  (2  P  2 
or  1121);  and  of  a  Basal  Pinacoid  (0001).  Apatite. 

74,  76,  80-83,  104 

Fig.  318.  Hexagonal.  Compound  Form  showing  planes  of 
a  Primary  Prism  (10lO);  of  a  Secondary  Prism  (1120);  of 
a  Primary  Pyramid  (loll);  and  one  of  a  Basal  Pinacoid 
(0001).  Apatite 74,76,80,81,83,104 

Fig.  319.  Hexagonal.  Compound  Form  showing  planes  of 
a  Primary  Prism  (lolo);  of  a  Secondary  Prism  (1120);  of 
two  Primary  Pyramids  (loTl),  (2021);  two  Secondary 
Pyramids  (P  2  or  1122, 1121);  and  a  plane  of  a  Basal  Pina- 
coid (0001).  Apatite .74,76,80-83,104 


DESCRIPTIONS    OF    THE    PLATES.  235 

PAGE 

PLATE    XIV 

Fig.  320.  Hexagonal.  Compound  Form  showing  the  planes 
of  a  Secondary  Prism  (1120);  of  a  Positive  Rhombohe- 
dron  (loTl);  of  a  Secondary  Pyramid  (2243),  and  of  a 
Basal  Pinacoid  (0001).  Corundum,  ...  74,  76,  80,  81,  83, 104 

Fig.  321.  Hexagonal.  Compound  Form  showing  the  plane 
of  a  Primary  Prism  (1010);  of  the  two  Primary  Pyramids 
(P  or  lOll,  2P  or  2021);  of  a  Secondary  Pyramid  (2P2  or 
1121);  of  a  Dihexagonal  Pyramid  (3P3/2  or  2131),  and 
one  of  a  Basal  Pinacoid  (0001).  Beryl  ...  74,  76,  80,  83, 104 

Fig.  322.  Hexagonal.  Compound  Form  showing  the  planes 
of  a  Primary  Prism  (1010);  a  Secondary  Prism  (1120);  a 
Tertiary  Prism  (2130);  two  Primary  Pyramids  (loll, 
2021);  two  Secondary  Pyramids  (1122, 1121);  a  Tertiary 
Pyramid  (2131),  and  a  Basal  Pinacoid  (0001 ),  74,  76, 80-83, 104 

Fig.  323.  Hexagonal.  Compound  form  showing  the  planes 
of  a  Primary  Prism  (1010);  a  Secondary  Prism  (1120); 
three  Primary  Pyramids  (loTl,  10l2,  2021);  three  Second- 
ary Pyramids  (1121,  1122,  2241),  and  a  Basal  Pinacoid 
(0001) 74,  76,  80, 103, 104 

Fig.  324.  Hexagonal.  Hemimorphic.  Tourmaline  Type. 
A  Compound  Form  showing  the  planes  of  a  Secondary 
Prism  (1120);  a  Primary  Trigonal  Prism  (lolO);  a  Pri- 
mary Rhombohedron  «•{  1011  }• ,  and  a  Secondary  Rhom- 
bohedron ™ ,{  OU2  }•  74,76,80,103,104 

Fig.  325.  Hexagonal.  Simple  Form.  A  Ditrigonal  Pyra- 
mid «•{  hkil  \  ...  .  ,.  .  ....  ..,  f  > 95,  104 

Fig.  326.  Hexagonal.  Simple  Form.  A  Dihexagonal  Pyra- 
mid (hkll) 95, 104 

Fig.  327.  Hexagonal.  Compound  Form.  A  Hemimorphic 
Form  of  the  Periodate  Type  showing  the  planes  of  a 
Positive  Primary  Trigonal  Pyramid  KT^  loTl  }• ;  a  Nega- 
tive Primary  Trigonal  Pyramid  KT  ^  0221  }• ;  a.  Negative 
Secondary  Trigonal  Pyramid  KT  ]  OlT2  }• ,  and  a  Tertiary 
Trigonal  Pyramid  Kr^54i9  j- 104 


236  DESCRIPTIONS   OF    THE    PLATES. 

PAGE 

Tig.  328.  Isometric.  Simple  Form.  Hexahedron  or  Cube 
(100) 123, 126 

Fig.  329.  Isometric.  Simple  Form.  Dodecahedron  (110), 

123,  127 

Fig.  330.  Isometric.  Simple  Form.  Tetrakis  Hexahedron 
(210) 123, 127 

Fig.  331.  Isometric.  Simple  Form.  Trigonal  Triakis  Octa- 
hedron (221) 123,  129 

Fig.  332.  Isometric.  Simple  Form.  Tetragonal  Triakis 
Octahedron  (211)'.- 123,129 

Fig.  333.  Isometric.  Simple  Form.  Tetragonal  Triakis 
Octahedron  (311) .  123, 129 

Fig.  334.  Isometric.  Simple  Form.  Hexakis  Octahedron 
(312) 123,  130 

Fig.  335.  Isometric.  Simple  Form.  Hexakis  Octahedron 
(421) 123, 130 

Fig.  336.  Isometric.  Simple  Form.  Cube  (100)  showing 
the  Cubic  or  Crystallographic  Axes  (a)  and  the  Octahe- 
dral Axes  (6)  drawn  in 123, 126, 131 

Fig.  337.  Isometric.  Simple  Form.  Cube  (100)  showing 
the  Dodecahedral  Axes  (c)  drawn  in 123, 131 

Fig.  338.  Isometric.  Simple  Form.  Octahedron  (111)  with 
the  alternate  planes  lined  to  show  the  derivation  of  the 
Tetrahedron  «<{  111  }•  .  . 123,128,131,132 

Fig.  339.  Isometric.  Simple  Form.  Tetrahedron  *•{  111  }> 
showing  the  inscribed  Octahedron  (111)  from  which  it 
was  derived  .  .  123, 128,  131, 132 

PLATE  XV 

Fig.  340.  Isometric.  Simple  Form.  Positive  Tetrahedron 
«•{  HI  }• 123,  131,  132 

Fig.  341.  Isometric.  Simple  Form.  Negative  Tetrahe- 
dron /c<{  ill  }• 123,  131,  132 

Fig.  342.  Isometric.    Simple  Form.    Trigonal  Triakis  Oc- 


DESCRIPTIONS    OF    THE    PLATES.  237 

PAGE 

tahedron  (332)  with  its  alternate  sets  of  three  planes  lined 
to  show  the  method  of  derivation  of  the  Tetragonal 
Triakis  Tetrahedron  « <{  hhl\  . 123,131,133 

Fig.  343.  Isometric,  Simple  Form.  Tetragonal  Triakis 
Tetrahedron  K  \  hhl  \  with  the  Trigonal  Triakis  Octahe- 
dron (hhl],  from  which  it  is  derived,  inscribed  .  .  123, 131, 133 

Fig.  344.  Isometric.  Simple  Form.  Positive  Tetragonal 
Triakis  Tetrahedron  *\  332  \ 123,131,133 

Fig.  345.  Isometric.  Simple  Form.  Negative  Tetragonal 
Triakis  Tetrahedron  *\  332  \  .• 123,131,133 

Fig.  340.  Isometric.  Simple  Form.  Tetragonal  Triakis 
Octahedron  (211)  with  its  alternate  sets  of  three  planes 
lined  to  show  the  method  of  derivation  of  the  Trigonal 
Triakis  Tetrahedron  «{  hll  \ 123,131,134 

Fig.  347.  Isometric.  Simple  Form.  Trigonal  Triakis  Tetra- 
hedron n{hll\  with  the  Tetragonal  Triakis  Octahedron 
(hll),  from  which  it  is  derived,  inscribed 123, 131, 134 

Fig.  348.  Isometric.  Simple  Form.  Positive  Trigonal 
Triakis  Tetrahedron  *  \2\l\ 123,131,134 

Fig.  349.  Isometric.  Simple  Form.  Negative  Trigonal 
Triakis  Tetrahedron  K\  211  }• 123,131,134 

Fig.  350.  Isometric.  Simple  Form.  Hexakis  Octahedron 
(hkl)  with  its  alternate  sets  of  six  planes  lined  to  show  the 
derivation  of  the  Hexakis  Tetrahedron  K\  hkl  }>  .123, 131, 134 

Fig.  351.  Isometric.  Simple  Form.  Hexakis  Tetrahedron 
K\  hkl  }•  with  the  Hexakis  Octahedron  (tiki),  from  which 
it  is  derived,  inscribed  .-.;.. 123,131,134 

Fig.  352.  Isometric.  Simple  Form.  Positive  Hexakis 
Tetrahedron  *\  521  \ ! 123,131,134 

Fig.  353.  Isometric.  Simple  Form.  Negative  Hexakis 
Tetrahedron  K  <j  521  }• 123,135 

Fig.  354.  Isometric.  Simple  Form.  Tetrakis  Hexahedron 
(/jfeO)  with  half  its  planes  lined  to  show  the  method  of 
derivation  of  the  Pentagonal  Dodecahedron  TT  •{  hko  }• ,  123,  136 


238  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Fig.  355.  Isometric.  Simple  Form.  Pentagonal  Dodeca- 
hedron TT-{  hkO  }>  with  an  inscribed  Tetrakis  Hexahedron 
(MO),  from  which  it  is  derived 123,136 

Fig.  356.  Isometric.  Simple  Form.  Positive  Pentagonal 
Dodecahedron  *  -j  hkQ  j> 123,  135-137 

Fig.  357.  Isometric.  Simple  Form.  Negative  Pentagonal 
Dodecahedron  K\  khQ  }• 123,  135-137 

Fig.  358.  Isometric.  Simple  Form.  Positive  Pentagonal 
Dodecahedron  *  1  /ifcO  }• 123,135,136 

Fig.  359.  Isometric.  Simple  -Form.  Positive  Pentagonal 
Dodecahedron  Tr-j/ifcO  }> 123,135,136 

Fig.  360.  Isometric.  Simple  Form.  Hexakis  Octahedron 
(hkl).  One  half  of  its  planes  are  lined  to  show  the 
method  of  derivation  of  the  Dyakis  Dodecahedron 
HfofeZ}- 123,137 

Fig.  361.  Isometric.  Simple  Form.  Dyakis  Dodecahedron 
TT  ]  likl  \  with  an  inscribed  Hexakis  Octahedron  (hkl), 
from  which  it  is  derived 123,137 

Fig.  362.  Isometric.  Simple  Form.  Positive  Dyakis  Dode- 
cahedron K\  321  }• 123,  137 

Fig.  363.  Isometric.  Simple  Form.  Negative  Dyakis  Do- 
decahedron TT  \  23i\. 123, 137 

Fig.  364.  Isometric.  Simple  Form.  Positive  Dyakis  Do- 
decahedron TT  ^  421  }• 123,  137 

Fig.  365.  Isometric.  Simple  Form.  Hexakis  Octahedron 
(hlcl)  with  its  alternate  planes  lined  to  indicate  the  method 
by  which  the  Pentagonal  Icositetrahedron  y  \  hkl  \  is  de- 
rived from  it  . 123,  138 

PLATE    XVI 
Fig.  366.    Isometric.    Simple  Form.    Positive  Pentagonal 

Icositetrahedron  y  \  hkl  \ 123,138 

Fig.  367.  Isometric.    Simple  Form.    Negative  Pentagonal 

Icositetrahedron  y  \  Ikh  }- 123,138 


DESCRIPTIONS    OP    THE    PLATES.  239 

PAGE 

Fig.  368.  Isometric.  Simple  Form.  Hexakis  Octahedron 
(hkl)  with  each  alternate  plane  in  each  alternate  octant 
lined  to  show  the  method  by  which  the  Tetrahedral  Pent- 
agonal Dodecahedron  KT-J  hkl  }-  is  derived  from  it.  See 
page  140 123 

Fig.  369.  Isometric.  Simple  Form.  Positive  Tetrahedral 
Pentagonal  Dodecahedron  KT-{  hkl  }• 123,141 

Fig.  370.  Isometric.  Simple  Form.  Negative  Tetrahedral 
Pentagonal  Dodecahedron  KT-{  Ikh  }• 123,141 

Fig.  371.  Isometric.  Compound  Form.  An  Octahedron 
(111)  truncating  the  solid  angles  of  an  inscribed  Cube 
(100) 123, 141 

Fig.  372.  Isometric.  Compound  Form.  A  Cube  (100)  with 
its  solid  angles  truncated  by  the  planes  of  an  Octahedron 
(111) 123, 141 

Fig.  373.  Isometric.  Compound  Form.  A  Cube  (100)  trun- 
cating the  solid  angles  of  the  inscribed  Octahedron  (111), 

123, 141 

Fig.  374.  Isometric.  -  Compound  Form.  An  Octahedron 
(111)  with  its  solid  angles  truncated  by  the  Cube  planes 
(100) •  • 123,141 

Fig.  375.  Isometric.  A  Cube  (100)  with  its  solid  angles 
truncated  by  the  planes  of  an  Octahedron  (111).  In  this 
case  where  the  planes  of  both  forms  are  equally  developed 
the  form  is  commonly  called  a  Cubo-Octahedron  .  .  123, 141 

Fig.  376.  Isometric.    Compound  Form.    A  Dodecahedron 

(110)  with  its  terminal  solid  angles  truncated  by  the  planes 

of  a  Cube  (100) 123,141 

Fig.  377.  Isometric.  Compound  Form.  A  Cube  (100)  with 
its  edges  truncated  by  the  planes  of  a  Dodecahedron 

(110) 123, 141 

Fig.  378.    Isometric.    Compound  Form.    An  Octahedron 

(111)  with  its  edges  truncated  by  the  planes  of  a  Dodeca- 
hedron (110) 123, 141 


240  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Fig.  379.  Isometric.    Compound  Form.    A  Dodecahedron 

(110)  with  itstriedral  solid  angles  truncated  by  the  planes 

of  an  Octahedron  (111) 123,141 

Fig.  380.  Isometric.  Compound  Form.  A  Cube  (100)  with 
its  solid  angles  truncated  by  the  planes  of  an  Octahedron 

(111)  and  its  edges  truncated  by  the  planes  of  a  Dodecahe- 
dron (110) 123,  141 

Fig.  381.  Isometric.  Compound  Form.  A  Cube  (100)  with 
its  edges  beveled  by  the  planes  of  a  Tetrakis  Hexahedron 
(hko) 123, 141 

Fig.  382.  Isometric.  Compound  Form.  An  Octahedron 
(111)  with  its  solid  angles  replaced  by  the  planes  of  a 
Tetrakis  Hexahedron  (hko) 123, 141 

Fig.  383.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  with  its  terminal  solid  angles  replaced  by  the  planes 
of  a  Tetrakis  Hexahedron  (hko) 123, 141 

Fig.  384.  Isometric.  Compound  Form.  A  Cube  (100)  with 
its  solid  angles  replaced  by  the  planes  of  a  Trigonal  Triakis 
Octahedron  (hhl) 123, 141 

Fig.  385.  Isometric.    Compound  Form.    A  Dodecahedron 

(110)  with  its  solid  triedral  angles  modified  by  the  planes 

of  a  Trigonal  Triakis  Octahedron  (hhl) 123, 141 

PLATE  XVII 

Fig.  386.  -Isometric.    Compound  Form.    An  Octahedron 

(111)  with  its  solid  angtes  replaced  by  the  planes  of  a 
Tetragonal  Triakis  Octahedron  (hll) 123, 141 

Fig.  387.  Isometric.  -Compound  Form.  A  Cube  with  its 
solid  angles  modified  by  the  planes  of  a  Tetragonal 
Triakis  Octahedron  (211) 123,  126, 141 

Fig.  388.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  with  its  edges  truncated  by  the  planes  of  a  Tetra- 
gonal Triakis  Octahedron  (211)  123,141 


DESCRIPTIONS    OF    THE    PLATES.  241 

PAGE 

Fig.  389.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  with  its  terminal  solid  angles  replaced  by  the  planes 
of  a  Tetragonal  Triakis  Octahedron  (/iZZ) 123, 141 

Fig.  390.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  with  its  triedral  solid  angles  replaced  by  the  planes 
of  a  Tetragonal  Triakis  Octahedron  (Ml) 123,  141 

Fig.  391.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  with  its  terminal  solid  angles  replaced  by  the  planes 
of  a  Hexakis  Octahedron  (hkl) 123, 141 

Fig.  392.  Isometric.    Compound  Form.    A  Dodecahedron 

(110)  with  its  triedral  angles  replaced  by  the  planes  of  a 
Hexakis  Octahedron  (hkl) 123, 141 

Fig.  393.  Isometric.    Compound  Form.    An  Octahedron 

(111)  with  its  solid  angles  replaced  by  the  planes  of  a 
Hexakis  Octahedron  (321) 123, 141 

Fig.  394.  Isometric.  Compound  Form.  A  Cube  (100)  with 
its  solid  angles  replaced  by  the  planes  of  a  Hexakis  Octa- 
hedron (421) 123, 141 

Fig.  395.  Isometric.  Compound  Form.  An  Octahedron 
(111)  with  its  solid  angles  truncated  by  the  planes  of  a 
Cube  (100),  and  modified  by  the  planes  of  a  Tetragonal 
Triakis  Octahedron  (211) 123, 141 

Fig.  396.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  with  its  triedral  solid  angles  truncated  by  the 
planes  of  an  Octahedron  (111),  and  its  terminal  solid 
angles  replaced  by  the  planes  of  a  Tetragonal  Triakis 
Octahedron  (311) 123, 141 

Fig.  397.  Isometric.    Compound  Form.    A  Dodecahedron 

(110)  with  its  triedral  angles  truncated  by  the  planes  of 
an  Octahedron  (111),  and  its  edges  beveled  by  the  planes 

of  a  Tetragonal  Triakis  Octahedron  (211) 123,141 

Fig.  398.  Isometric.    Compound  Form.    An  Octahedron 

(111)  with  its  edges  truncated  by  the  planes  of  a  Dodeca- 
hedron (110),  and  its  solid  angles  replaced  by  the  planes 


242  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

of  a  Cube  (100),  and  by  the  planes  of   a  Tetragonal 
Triakis  Octahedron  (211) 123.141 

Tig.  399.  Isometric.  Compound  Form.  A  Tetragonal 
Triakis  Octahedron  (211)  modified  by  the  planes  of  a 
Cube  (100);  the  planes  of  a  Dodecahedron  (110),  and  the 
planes  of  an  Octahedron  (111)  . 123,141 

Fig.  400.  Isometric.  Compound  Form.  An  Octahedron 
(111)  modified  by  the  planes  of  a  Dodecahedron  (110);  of 
a  Tetragonal  Triakis  Octahedron  (hll)-,  a  Tetrakis  Hexa- 
hedron (M-0),  and  a  Hexakis  Octahedron  (hkl)  ....  123, 141 

IFig.  401.  Isometric.  Compound  Form.  A  Positive  Tetra- 
hedron K-{  111  }-  modified  by,  a  Negative  Tetrahedron 
KflTl  1- 123,141 

JFig.  402.  Isometric.  Compound  Form.  A  Positive  Tetra- 
hedron K-{  111  [-  modified  by  the  planes  of  a  Negative 
Tetrahedron  «-{  111  }-  .  .  .  . 123, 141 

JTig.  403.  Isometric.  Compound  Form.  A  Positive  Tetra- 
hedron K-{  ill  }•  with  its  edges  truncated  by  the  planes  of 
a  Cube  (100) 123, 141 

Pig.  404.  Isometric.  Compound  Form.  A  Positive  Tetra- 
hedron /c-j  111  }-  modified  by  the  planes  of  a  Dodecahedron 
K-l  ifo^ 123,141 

Fig.  405.  Isometric.  Compound  Form.  A  Positive  Tetra- 
hedron K-{  ill  }-  with  its  edges  beveled  by  the  planes  of  a 
Cube  (100)  and  its  solid  angles  replaced  by  the  planes  of  a 
Dodecahedron  « -{  110  }- 123,141 

Fig.  406.  Isometric.  Compound  Form.  A  Positive  Tetra- 
hedron K-{  ill  }.  with  its  edges  truncated  by  the  planes  of 
a  Cube  (100),  and  its  solid  angles  replaced  by  the  planes 
of  a  Negative  Tetrahedron  «•{  ifl  }•  and  the  planes  of  a 

Dodecahedron  «-{  110  }• 123,141 

Fig.  407.  Isometric. '  Compound  Form.  A  Positive  Tetra- 
hedron /c-j  ill  }•  with  its  edges  beveled  by  the  planes  of  a 
Trigonal  Triakis  Tetrahedron  K  -j  211  }- 123,141 


DESCRIPTIONS    OF    THE    PLATES.  243 

PAGE 

Tig.  408.  Isometric.  Compound  Form.  A  Positive  Tetra- 
hedron *-{  111  }•  with  its  edges  beveled  by  the  planes  of  a 
Trigonal  Triakis  Tetrahedron  «-{211}-,  and  its  solid 
angles  replaced  by  the  planes  of  a  Dodecahedron  *•{  110  }- . 

123, 141 

Tig.  409.  Isometric.  Compound  Form.  A  Positive  Tetra- 
hedron K-{  ill  }-  with  its  edges  beveled  by  the  planes  of  a 
Trigonal  Triakis  Tetrahedron  «-{  211  }•  and  its  solid  angles 
replaced  by  the  planes  of  a  Dodecahedron  *\  110  } ,  and 
the  planes  of  a  Negative  Trigonal  Tetrahedron  *\  211  \ , 

123, 141 

Fig.  410.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  with  its  terminal  angles  truncated  by  the  planes  of 
a  Cube  (100)  and  its  alternate  Triedral  angles  truncated 
by  the  planes  of  a  Tetrahedron  *{  111  }• 123,141 

Fig.  411.  Compound  Form.  A  Tetrahedron  K\  111  \  modi- 
fied by  the  planes  of  a  Trigonal  Triakis  Tetrahedron 
*\Ul\ •. 123,141 

Fig.  412.  Isometric.  Compound  Form.  A  Cube  with  its 
alternate  solid  angles  truncated  by  the  planes  of  a  Tetra- 
hedron K\\\\\ 123,  141 

Fig.  413.  Isometric.  Compound  Form.  A  Cube  (100)  with 
its  edges  truncated  by  the  planes  of  a  Dodecahedron 
(110)  and  its  angles  alternately  replaced  by  the  planes  of 
a  Positive  Tetrahedron  K\  ill  }- ,  and  of  a  Negative  Tetra- 
hedron *\U\\ 123, 141 

Fig.  414.  Isometric.  Compound  Form.  A  Cube  (100) 
with  its  edges  truncated  by  the  planes  of  a  Dodecahedron 
(110)  and  its  solid  angles  alternately  replaced  by  the  planes 
of  a  Positive  Tetrahedron  K\  ill  }-  and  a  Hexakis  Tetra- 
hedron K  «{  531  }- ,  and  by  a  Negative  Tetrahedron  K  •{  ill  }• , 

123,  141 

Fig.  415.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  with  its  alternate  edges  modified  by  the  planes  of  a 
Negative  Trigonal  Triakis  Tetrahedron  « -{  Jill  }•  .  .  .  123, 141 


244  DESCRIPTIONS    OF    THE    PLATES. 


PLATE  XVIII 

Fig.  416.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  with  its  terminal  solid  angles  modified  by  the 
planes  of  a  Hexakis  Tetrahedron  K  -\hkl\-  .....  123,  141 

Fig.  417.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  modified  by  the  planes  of  a  Trigonal  Triakis  Tetra- 
hedron «•{  211  }-  ...................  123,  141 

Fig.  418.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  modified  by  the  planes  of  a  Hexakis  Tetrahedron 
K^hJcl}-  .......................  123,  141 

Fig.  419.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  modified  by  the  planes  of  a  Trigonal  Triakis  Tetra- 
hedron K\hll\  .  .  .................  123,  141 

Fig.  420.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  modified  by  the  planes  of  a  Trigonal  Triakis  Tetra- 
hedron K  1  hll  \  ...................  123,143 

Fig.  421.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  modified  by  the  Tetragonal  Triakis  Octahedron 
*  \hhl\-  .......................  123,  141 

Fig.  422.  Isometric.  Compound  Form.  A  Dodecahedron 
(110)  with  its  terminal  solid  angles  truncated  by  the 
planes  of  a  Cube  (100)  and  its  alternate  Trigonal  Angles 
truncated  by  the  planes  of  a  Tetrahedron  n\  111  }-  .  .  123,  141 

Fig.  423.  Isometric.  Compound  Form.  A  Positive  Tri- 
gonal Triakis  Tetrahedron  «  \  hll  \  modified  by  the  planes 
of  a  Cube  (100);  of  a  Negative  Trigonal  Triakis  Tetra- 
hedron K\  Jill  }•  ;  of  a  Tetrahedron  /c-|  111  }•  ;  of  a  Dodeca- 
hedron (110);  of  a  Tetrakis  Hexahedron  (/ifcO);  and  of  a 
Negative  Hexakis  Tetrahedron  K  ^  h~kl  }•  .......  123,141 

Fig.  424.  Isometric.  Compound  Form.  A  Pentagonal 
Dodecahedron  JT-{  120  }•  modified  by  the  planes  of  a  Cube 
(100)  ........................  ]23,  141 

Fig.  425.  Isometric.    Compound  Form.    A  Cube  (100)  with 


DESCRIPTIONS    OF    THE    PLATES.  245 

PAGE 

its  edges  truncated  by  the  planes  of  a  Pentagonal  Dodeca- 
hedron TT  •{  120  }• ,  and  its  solid  angles  truncated  by  the 
planes  of  an  Octahedron  (111) 123,141 

Pig.  426.  Isometric.  Compound  Form.  A  Cube  (100) 
modified  by  the  planes  of  an  Octahedron  (111),  and  of  a 
Pentagonal  Dodecahedron  TT  ^  120  j- 123,141 

Fig.  427.  Isometric.  Compound  Form.  An  Octahedron 
(111)  with  its  solid  angles  modified  by  the  planes  of  a 
Pentagonal  Dodecahedron  *•-{  120  }- 123y  141 

Fig.  428.  Isometric.  Compound  Form.  A  Pentagonal 
Dodecahedron  K\  120  \  modified  by  the  planes  of  an 
Octahedron  (111) 123, 141 

Fig.  429.  Isometric.  Compound  Form.  A  Pentagonal 
Dodecahedron  TT{  120  }•  .  modified  by  the  planes  of  an 
Octahedron  (111) 123, 141 

Fig.  430.  Isometric.  Compound  Form.  A  Pentagonal 
Dodecahedron  *  \  120  J-  modified  by  the  planes  of  a  Penta- 
gonal Dodecahedron  *  \  320  \ 123, 141 

Fig.  431.  Isometric.  Compound  Form.  A  Cube  (100)  with 
its  solid  angles  modified  .by  the  planes  of  a  Dyakis  Dode- 
cahedron TT  \  likl  \ 123,141 

Fig.  432.  Isometric.  Compound  Form.  Pentagonal  Dode- 
cahedron TT  \  120  \ .  modified  by  .the  planes  of  a  Dyakis 
Dodecahedron  K\  142  \ 123,141 

Fig.  433.  Isometric.  Compound  Form.  A  Pentagonal 
Dodecahedron  K\  120  \  modified  by  the  planes  of  a  Tetra- 
gonal Triakis  Octahedron  (211)  123,141 

Fig.  434.  Isometric.  Compound  Form.  A  Pentagonal 
Dodecahedron  w  \  120  \  modified  by  the  planes  of  a  Dyakis 
Dodecahedron  *\  123  \ 123,141 

Fig.  435.  Isometric.  Compound  Form.  A  Pentagonal 
Dodecahedron  w  \  120  }  modified  by  the  planes  of  a  Dyakis 
Dodecahedron  TT  \  123  \ 123,141 

Fig.   436.    Isometric.     Compound  Form.     A  Pentagonal 


246  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Dodecahedron  K\  120  \  modified  by  the  planes  of  another 
Pentagonal  Dodecahedron  *\  130  }- 123,141 

Fig.  437.  Isometric.  Compound  Form.  A  Positive  Penta- 
gonal Dodecahedron  K\  120  }•  modified  by  the  planes  of  a 
Negative  Pentagonal  Dodecahedron  K  \  khQ  }•  .  .  .  .123,141 

Fig.  438.  Isometric.  Compound  Form.  A  Dyakis  Dode- 
cahedron 7r<(  132  }>  modified  by  the  planes  of  a  Cube  (100). 

123,  141 

Fig.  439.  Isometric.  Compound  Form.  A  Dyakis  Dode- 
cahedron TT  -{  421  }•  modified  by  the  planes  of  a  Pentagonal 
Dodecahedron  TT<|  210  }- 123,141 

Fig.  440.  Isometric.  Compound  Form.  An  Octahedron 
(111),  with  its  solid  angles  modified  by  the  planes  of  a 
Dyakis  Dodecahedron  *\  123  \ 123,141 

Fig.  441.  Isometric.  Compound  Form.  A  Negative  Penta- 
gonal Dodecahedron  K  \  102  \  modified  by  the  planes  of  a 
Negative  Dodecahedron  *  \  123  \ 123,141 

Fig.  442.  Isometric.  Compound  Form.  A  Pentagonal 
Dodecahedron  K  \  120  \  modified  by  the  planes  of  a  Dyakis 
Dodecahedron  *  \  142  \ 123,141 

Fig.  443.  Isometric.  Compound  Form.  A  Pentagonal 
Dodecahedron  K  \  hkQ  [  modified  by  the  planes  of  a  Dyakis 
Dodecahedron  TT  «{  hkl  }- 123,141 

Fig.  444.  Isometric.  Compound  Form.  An  Octahedron 
(111)  with  its  solid  angles  modified  by  the  planes  of  a 
Cube  (100);  a  Tetragonal  Triakis  Octahedron  (121);  and 
by  a  Pentagonal  Dodecahedron  TT«|  120  }• ,  and  its  edges 
truncated  by  the  planes  of  a  Dodecahedron  (110)  .  .  .  123, 141 

Fig.  445.  Isometric.  Compound  Form.  A  Cube  (100) 
modified  by  the  planes  of  a  Tetragonal  Triakis  Octa- 
hedron (211);  a  Dyakis  Dodecahedron  TT-|  132  }> ;  a  second 
Dyakis  Dodecahedron  *  \U2\-,  a  Pentagonal  Dodeca- 
hedron TTHJ  210  \ ;  and  an  Octahedron  (111) 123, 141 


DESCRIPTIONS    OF    THE    PLATES.  247 

PAGE 

PLATE  XIX 

Fig.  446.  A  Mineral  Aggregate  composed  of  irregular 
grains  joined  together  and  forming  one  compound  mass.  149 

Figs.  447,  448,  449,  450,  and  451.  These  figures  (110,  111) 
illustrate  different  types  of  Parallel  Growths 149 

Fig.  452.  Isometric.  A  Cubical  Form  (100)  produced  by 
the  joining  together  along  the  diagonals  of  the  cubic 
faces  of  parts  of  four  Cubes  (100) 149,151 

Fig.  453.  Isometric.  A  Cubical  Form  (100)  composed  of 
parts  of  four  cubical  forms  united  along  the  diagonals  of 
the  cube  faces.  Each  of  the  four  parts  is  made  up  of  a 
series  of  parallel  growths  forming  an  Oscillatory  Com- 
bination   149, 151 

Figs.  454,  455, 456, 457.  Isometric.  Cubes  (100)  and  Penta- 
gonal Dodecahedrons  K\  hkQ  }•  showing  various  Oscilla- 
tory Combinations 149, 151 

Fig.  458.  Orthorhombic.  Compound  Form  (110,  100,  Okl) 
showing  a  simple  twinned  form,  Aragonite 150, 153 

Figs.  459,  460,  461.  Orthorhombic.  Compound  Forms 
(110)  showing  Polysynthetic  Twinning  .  .  .  -150,151,153 

Fig.  462.  Triclinic.  Cleavage  Plate  showing  Polysynthetic 
Twinning 151 

Fig.  463.  Isometric.  Simple  Form.  Octahedron  (111) 
showing  a  Twinning  Plane  (vibcdef) 149, 152 

Fig.  464.  Isometric.  A  Contact  Twin  Form.  (Octahedral, 
111)  produced  by  turning  part  of  the  crystal  (Fig.  463) 
half  way  around  upon  the  Twinning  Plane  (afcccZe/), 

149, 150, 152 

Fig.  465.  Isometric.  Simple  Form.  Octahedron  (111) 
showing  Twinning  Plane  (alcdef) 149,152 

Fig.  466.  Isometric.  A  Contact  Twin  Form  (Octahedral, 
111)  produced  by  revolving  one  part  of  Fig.  465  half  way 
around  upon  the  Twinning  Plane  (abcdef)  ....  149, 150, 152 

Figs.  467,  468.  Isometric.  Octahedral  (111)  Contact  Twin 
Forms 149, 150,  152 


248  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Fig.  469.  Isometric.  Simple  Form.  A  Cube  (100)  show- 
ing a  Twinning  Plane  (abcdef) 149, 152 

Fig.  470.  Isometric.  A  Contact  Twinned  Cube  (100) 
formed  by  turning  one  part  of  Fig.  469  one  half  way 
around  upon  the  Twinning  Plane  (abcdef) ....  149,  150, 152 

Fig.  471.  Isometric.  Simple  Form.  A  Dodecahedron  (110) 
showing  a  Twinning  Plane  (abcdef) 149, 150, 152 

Fig.  472.  Isometric.  A  Contact  Twinned  Dodecahedron 
(110)  produced  by  turning  one  part  of  Fig.  471  one-half 
way  around  on  the  Twinning  Plane  (abcdef)  .  .  149, 150, 151 

PLATE  XX 

Fig.  473.  Isometric.  A  Dodecahedron  (110)  showing  a 
Twinning  Plane  (alcdef) 149, 150, 152 

Fig.  474.  Isometric.  A  Contact  Twinned  Dodecahedron 
(100)  produced  by  turning  one  part  of  Fig.  473  around  for 
180°  on  the  Twinning  Plane  (abcdef) 149,150,152 

Fig.  475.  Isometric.  Simple  Form.  A  Tetrakis  Hexa- 
hedron (fcfcO)  showing  a  Contact  Twinning  Plane 
(dbcdefgliijK). 149, 152 

Fig.  476.  Isometric.  A  Contact  Twinned  Tetrakis  Hexa- 
hedron (/i/cO)  produced  by  turning  one  part  of  Fig.  475  on 
the  Contact  Twinning  Plane  (abcdefyhijk)  for  a  distance, 
of  180° 149,  150,  152 

Fig.  477.  Isometric.    A  Contact  Twinned  Cube  (100), 

149,  150,  152 

Fig.  478.  Isometric.  Simple  Form.  A  Cube  (100)  showing 
a  Contact  Twinning  Plane  (abcdef)  ........  149, 152 

Fig.  479.  Isometric.  A  Contact  Twinned  Cube  (100)  pro- 
duced by  revolving  one  part  of  Fig.  478  on  the  Contact 
Twinning  Plane  (abcdefy  through  an  angle  of  180°, 

149,  150,  152 

Fig.  480.  Monoclinic.  A  Compound  Form  (111,  110,  010) 
showing  a  Contact  Twinning  Plane  (abcdcf).  Gypsum.  149, 152 


DESCRIPTIONS    OF   THE   PLATES.  249 

PAGE 

Fig.  481.  Monoclinic.  A  Contact  Twin  Form  produced 
by  revolving  one-half  of  Fig.  480  through  an  angle  of  180° 
upon  the  Twinning  Plane  (abcdef).  This  gives  the  com- 
mon spear-  or  arrow-head  form  of  Gypsum.  .  .  .  149, 150, 152 

Fig.  482.  Hexagonal.  A  spear-  or  arrow-head  form  of  a 
Scalenohedron  produced  by  revolving  one-half  of  the 
crystal  through  an  angle  of  180°  about  a  Contact  Plane 
(dbcdefgh).  Calcite 149, 150, 152 

Fig.  483.  Monoclinic.  A  spear-  or  arrow-head  form  pro- 
duced by  the  rotation  of  one-half  of  the  crystal  about  the 
Contact  Twinning  Plane  (abcdef).  Gypsum.  .  .  149,  150, 152 

Fig.  484.  Triclinic.  A  Contact  Twinned  Form  produced 
by  the  turning  of  one  part  180°  upon  the  Twinning  Plane 
(abcdef).  Albite 149, 150, 152 

Fig.  485.  Monoclinic.  A  Contact  Twinned  Crystal  formed 
by  the  rotation  of  one  part  upon  the  Twinning  Plane 
(abcdef)  through  an  angle  of  180°.  Augite  .  .  .  149, 150, 152 

Fig.  486.  Monoclinic.  A  Contact  Twinned  Crystal  formed 
by  rotating  one  part  on  the  Twinning  Plane  (abcdef) 
through  an  angle  of  180°.  Orthoclase 149, 150,  152 

Fig.  487.  Monoclinic.  A  Compound  Form  (001,  110,  120, 
111)  with  a  Contact  Twinning  Plane  (abed)  drawn  in.  149, 152 

Fig.  488.  Monoclinic.  A  Contact  Twinned  Crystal  formed 
by  turning  one  part  of  Fig.  487  through  an  angle  of  180° 
upon  the  Twinning  Plane  (abed).  .  .  .  ..;.  .  .  .149,150,152 

Fig.  489.  Triclinic.  A  Compound  Crystal  Form  (001,010, 
110, 101,  111)  showing  a  Twinning  Plane  (abcdef)  drawn 
in.  Albite ^. ,  .  149,152 

Fig.  490.  Triclinic.  A  Contact  Twinned  Crystal  produced 
by  turning  part  of  Fig.  489  through  an  angle  of  180°  upon 
the  Contact  Twinning  Plane.  Albite  .....;..  149, 152 

Fig.  491 .  Monoclinic.  Crystal  showing  a  dividing  line  (a&) 
and  a  Contact  Twinning  Plane  (cdefgh).  Orthoclase.  149, 152 

Fig.  492.  Monoclinic.    The  crystal  is  the  same  as  Fig.  491, 


250  DESCRIPTIONS   OF   THE   PLATES. 

PAGE 

but  it  has  been  turned  around  180°.  The  dividing  line 
(afc)  and  the  Contact  Twinning  Plane  (cdefgh)  have  been 
drawn  in.  Orthoclase 149, 152 

Fig.  493.  Monoclinic.  A  Contact  Twinned  Crystal  produced 
by  uniting  the  front  half  of  Fig.  491  with  the  back  half  of 
Fig.  492  along  the  Contact  Plane  (cdefgh).  Orthoclase, 

149, 150, 152 

Fig.  494.  Monoclinic.  A  Contact  Twinned  Crystal  produced 
by  uniting  the  front  half  of  Fig.  492  with  the  back  half  of 
Fig.  491.  Orthoclase 149, 150, 152 

Fig.  495.  Orthorhombic.  A  Contact  Twinned  Crystal  pro- 
duced by  revolving  through  an  angle  of  180°  of  one  part  of 
Fig.  501  upon  the  Contact  Plane  (abcdef).  Aragonite, 

149,  150, 152 

Fig.  496.  Monoclinic.  A  Contact  Twinned  Crystal.  Ortho- 
clase  149, 152 

Fig.  497.  Monoclinic.  Crystal  with  the  Contact  Twinning 
Plane  (abcdef)  drawn  in 149, 152 

Fig.  498.  Monoclinic.  A  Contact  Twinned  Form  pro- 
duced by  turning  part  of  Fig.  497, 180°  about  the  Contact 
Plane  (abcdef) 149, 150, 152 

Fig.  499.  Hexagonal.  Contact  Twin  formed  by  the  growing 
together  of  two  Ehombohedrons,  E  and  E'.  Calcite, 

149, 150, 152 

Fig.  500.  Hexagonal.  Contact  Trilling  formed  by  the  union 
of  three  Bhombohedrons,  E,  R',  and  R".  Calcite.  149, 150, 152 

PLATE  XXI 

Fig.  501.  Orthorhombic.  The  Crystal  has  the  Contact 
Twinning  Plane  (abcdef)  drawn  in.  Aragonite  .  149, 150, 152 

Fig.  502.  Orthorhombic.  A  Contact  Twin  produced  by 
the  revolution  of  one-half  of  the  form  for  180°  upon  the 
Contact  Plane  (abcdef).  Aragonite 149,  150, 152 


DESCRIPTIONS    OF    THE    PLATES.  251 

PAGE 

Tig.  503.  Hexagonal.  A  Contact  Twin  Form  produced  by 
revolving  the  upper  half  of  a  Scalenohedron  « \  hkll  }• 
terminated  by  the  planes  of  a  Hexagonal  Pyramid  (hkll) 
through  an  angle  of  180°  upon  the  lower  half  of  the 
Scalenohedron  «-{  hkil  \  which  is  also  terminated  by  the 
planes  of  a  Hexagonal  Pyramid  (hkil).  Calcite  .  149, 150, 152 

Fig.  504.  Hexagonal.  A  Contact  Twin  Form  produced  by 
revolving  one-half  of  a  Scalenohedron  *  •{  hkll  }•  upon  the 
other  half  of  the  form.  The  Contact  Plane  is  parallel  to 
a  Basal  Pinacoid  (0001).  Calcite 149, 150,  152 

Fig.  505.  Hexagonal.  A  Contact  Twin  Form  showing  the 
Contact  Plane  (abed).  This  form  can  also  be  artificially 
produced  by  taking  a  cleavage  rhombohedron  of  Calcite. 
Then  press  one  of  the  terminal  edges  with  a  dull  knife 
blade.  As  the  knife  gradually  enters  the  Calcite  it  is 
slightly  pressed  towards  the  rhombohedral  apex,  when  a 
series  of  thin  laminae  glide  along  each  other  parallel  to 
the  Contact  Plane  (abed),  giving  rise  to  a  form  like  the 
one  here  represented.  This  is  Secondary  Twinning,  and 
the  planes  parallel  to  the  Contact  Twinning  Plane  (abed) 
are  known  as  Gliding  Planes  or  *'  Gleitflachen."  Calcite, 

149, 150,  152 

Fig.  506.  Hexagonal.  Contact  Twinned  Khombohedrons 
(B  and  B1)  joined  by  the  Contact  Plane  (abcde).  Calcite, 

149,  150,  152 

Fig.  507.  Hexagonal.  Contact  Twinned  Rhombohedrons 
(B  and  B')  joined  by  the  Contact  Twinning  Plane 
(abcde).  Calcite .  .  .  .149,150,152 

Fig.  508.  Tetragonal.  Compound  Form,  showing  the 
planes  of  a  Primary  Prism  (110),  with  its  lateral  edges 
truncated  by  the  planes  of  a  Secondary  Prism  (100)  and 
terminated  by  the  planes  of  a  Primary  Pyramid  (111)  and 
a  Secondary  Pyramid  (101).  A  Contact  Twinning  Plane 
(ab)  is  drawn  in.  Cassiterite 149,  150,  152 


252  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Fig.  509.  Tetragonal.  Compound  Contact  Twin  Form. 
The  same  figure  as  508,  showing  the  twinning  produced 
by  revolving  one  part  180°  around  the  plane  (a&).  Cas- 
siterite 149, 150, 152, 153 

Fig.  510.  Tetragonal.  Compound  Contact  Twin  Form 
similar  to  Fig.  510.  Cassiterite 149, 150, 152, 153 

Fig.  511.  Hexagonal.  Compound  Contact  Twin  Form 
showing  the  planes  of  a  Hexagonal  Prism  (1010)  termi- 
nated by  the  Basal  Planes  (0001,  OOOl),  and  twinned  along 
the  plane  (a&).  Calcite 149,  150, 152, 153 

Fig.  512.  Hexagonal.  Compound  Contact  Twin  Form 
showing  the  planes  of  a  Hexagonal  Prism  (1010),  termi- 
nated by  Basal  Planes  (0001,  0001),  and  twinned  along  the 
plane  (a&).  Calcite 149, 150, 152, 153 

Fig.  513.  Hexagonal.  A  Compound  Contact  Twin  Form 
similar  to  Fig.  512,  but  twinned  along  the  plane  (abcdef). 
Calcite 149, 150, 152, 153 

Fig.  514.  Tetragonal.  Compound  Contact  Twin  Form 
showing  the  planes  of  a  Primary  Prism  (110),  a  Secondary 
Prism  (100),  and  a  Primary  Pyramid  (111).  Cassiterite, 

149,  150, 152,  153 

Fig.  515.  Tetragonal.  A  Compound  Contact  Twin  Form 
showing  the  planes  of  a  Primary  Prism  (110),  a  Secondary 
Prism  (100),  and  a  Primary  Pyramid  (111).  Cassiterite, 

149, 150, 152 

Fig.  516.  Tetragonal.  A  Compound  Contact  Twin  show- 
ing the  planes  of  a  Ditetragonal  Prism  (310)  and  a  Pri- 
mary Pyramid  (111).  Kutile 149,150,152,153 

Fig.  517.  Tetragonal.  A.  Compound  Contact  Twin.  A 
Geniculated  Form  showing  the  planes  of  a  Ditetragonal 
Prism  terminated  by  the  planes  of  a  Primary  Pyramid 
(111).  The  form  is  twinned  along  the  planes  ab  and  cd. 
Rutile 149, 150,  152, 153 

Fig.   518.    Orthorhombic.     A   Compound  Contact   Twin 


DESCRIPTIONS    OF    THE    PLATES.  253 

PAGE 

Crystal,  twinned  about  the  plane  (abed)  and  showing  the 
planes  of  a  Prism  (210),  a  Brachy-Dome  (OM),  and  a 
Pyramid  (111) 149, 150, 152, 153 

Fig.  519.  Tetragonal.  A  Compound  Contact  Twin,  twin- 
ning along  the  plane  (a&)  and  showing  the  planes  of  a 
Primary  Pyramid  (111),  two  Secondary  Pyramids  (101, 
201)  and  two  Basal  Planes  (001,  GOT).  Chalcopyrite, 

149, 150,  152, 153 

Fig.  520.  Isometric.  Penetration  Twin  formed  by  the 
intergrowth  of  Octahedrons  (111).  Haiiynite, 

149,  150,  153 

Fig.  521.  Isometric.  Penetration  Twin  formed  by  the 
intergrowth  of  Tetrahedrons  «•{  111  }> .  Sphalerite, 

149, 150, 153 

Fig.  522.  Isometric.  A  Penetration  Twin  formed  by  the 
intergrowth  of  two  Hexahedrons  or  Cubes  (100).  Ga- 
lenite • 149,150,153 

Fig.  523.  Hexagonal.  A  Penetration  Twin  formed  by  the 
interpenetration  of  two  Khombohedrons  (loTl).  Chab- 
azite 149,150,153 

Fig.  524.  Isometric.  A  Penetration  Twin  formed  by  the 
intergrowth  of  two  Cubes  (100).  Galenite  .  .  .  149, 150, 153 

PLATE  XXII 

Fig.  525.  Isometric.    A  Penetration  Twin  Form  produced 

by  the  interpenetration  of  two  Cubes  (100).    Galenite, 

149,  150, 153 
Fig.  526.  Isometric.    A  Penetration  Twin  produced  by  the 

intergrowth  of  two  Cubes  (100).    Galenite    .  .  .  149,  150, 153 
Fig.  527.  Isometric.    Penetration  Twin.    Similar  to  Fig. 

526.    Fluorite 149, 150, 153 

Fig.  528.  Isometric.    Penetration  Twin.    Similar  to  Fig. 

525.    Galenite 149, 150, 153 


254  DESCRIPTIONS   OF    THE    PLATES. 

PAGE 

Fig.  529.  Isometric.  Penetration  Twin.  Similar  to  Fig. 
526.  Galenite 149, 150, 153 

Fig.  530.  Isometric.  Penetration  Twin.  Similar  to  Fig. 
529 149,  150,  153 

Fig.  531.  Isometric.  A  Penetration  Twin  formed  by  the 
intergrowth  of  two  Pentagonal  Dodecahedrons  K\  210  }• 
andTr^  120  }-.  Pyrite  . 149, 150, 153 

Fig.  532.  Isometric.  Penetration  Twin.  Similar  to  Fig. 
531.  Pyrite 149, 150, 153 

Fig.  533.  Isometric.  Penetration  Twin.  Similar  to  Fig. 
537.  Pyrite 149, 150, 153 

Fig.  534.  Isometric.  A  Penetration  Twin  produced  by  the 
intergrowth  of  a  Cube  (100)  and  the  two  Pentagonal 
Dodecahedrons  TT  ^  210  }•  and  K\  120  \- 149,  150, 153 

Fig.  535.  Isometric.  A  Penetration  Twin  formed  by  the 
interpenetration  of  Dodecahedrons  (110).  Sodalite, 

149, 150,  153 

Fig.  536.  Isometric.  A  Penetration  Twin  produced  by  the 
intergrowth  of  an  Octahedron  (111)  with  a  Dyakis  Dode- 
cahedron TT  •{  Tiki  \ 149,150,153 

Fig.  537.  Isometric.  A  Penetration  Twin  formed  by  the 
intergrowth  of  a  Tetrahedron  K\  111  }-,  a  Dodecahedron 
(110)  and  a  Trigonal  Triakis  Tetrahedron  /c-j211}>. 
Tetrahedrite .  .  .  149, 150, 153 

Fig.  538.  Isometric.  A  distorted  Penetration  Twin  formed 
by  the  intergrowth  of  an  Octahedron  (111)  and  a  Cube 
(100).  Galenite 149, 150, 153 

Fig.  539.  Isometric.  A  Penetration  Twin  produced  by  the 
interpenetration  of  two  Tetrahedrons  K\  111  \ ,  K\  ill  \ . 
Diamond 149, 150, 153 

Fig.  540.  Isometric.  A  Penetration  Twin  produced  by  the 
interpenetration  of  two  Tetrahedrons  «-{  ill  }-,  «•{  111  }-. 
Tetrahedrite 149, 150, 153 

Fig.  541.  Hexagonal.    A  Penetration  Twin  formed  by  the 


DESCRIPTIONS   OF   THE   PLATES.  255 

PAGE 

intergrowth  of  a  Primary  and  a  Secondary  Hexagonal 
Prism  (1010, 1120)  and  a  Positive  and  a  Negative  Rhombo- 
hedron^  loll  }-,«.{  0111  }-.  Quartz 149,150,153 

Fig.  542.  Hexagonal.  A  Penetration  Twin  produced  by 
the  intergrowth  of  two  crystals  showing  the  planes  of  a 
Primary  Prism  (lOTl)  and  two  Rhombohedrons  « •{  loll  }-, 
««{  Olll  }>.  Quartz  .  .,  . 149, 150,  153 

Fig.  543.  Hexagonal.  A  Penetration  Twin  made  by  the 
intergrowth  of  two  forms  showing  the  planes  of  a  Pri- 
mary Hexagonal  Prism  (10TO),  a  Bhombohedron  K -j  loll  }- , 
and  a  Dihexagonal  Pyramid  (5161).  Quartz  .  .  .  149, 150, 153 

Fig.  544.  Hexagonal.  A  Penetration  Twin  showing  the 
planes  of  a  Secondary  Pyramid  (2-2-I-3),  of  Rhombo- 
hedrons  «-{  loll  }• ,  and  of  Basal  Pinacoids  (0001).  Hem- 
atite . 149, 150, 153 

Fig.  546.  Hexagonal.  A  Penetration  Twin  composed  of 
intergrowths  of  Secondary  Hexagonal  Prisms  (1120) ,  and 
three  Rhombohedrons  «-{  loll  }• ,  «•{  0221  f ,  « \  Oll2  }• . 
Chabazite 149, 150, 153 

Fig.  546.  Monoclinic.  A  Penetration  Twin.  The  Twin- 
ning Plane  is  parallel  to  the  Clino-Pinacoid  (010).  The 
form  shows  the  planes  of  Basal-Pinacoids  (001),  Clino- 
Pinacoids  (010),  Hemi-Orthodomes  (201)  and  Prisms 
(110).  Orthoclase.  A  Carlsbad  Twin 149, 150, 153 

Fig.  547.  Monoclinic.    A  Penetration  Twin  similar  to  Fig. 

546.  A  Carlsbad  Twin.    Orthoclase  .  .  ,  .  .  .  149, 150, 153 
Fig.  548.  Monoclinic.    A  Penetration  Twin  similar  to  Fig. 

547.  A  Carlsbad  Twin.    Orthoclase 149,  150, 153 

PLATE  XXIII 

Fig.  549.  Monoclinic.  A  Penetration  Twin  produced  by 
the  intergrowth  of  Prisms  (110)  and  Clino-Pinacoids 
(010).  Resembles  closely  a  Tetragonal  Form.  Phillip- 
site  .  149,  150, 153 


256  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Fig.  550.  Monoclinic.  A  Penetration  Twin  similar  to  Fig. 
549.  Harmotome  ....  149, 150, 158 

Fig.  551.  Orthorhombic.  A  Penetration  Twin  showing 
the  planes  of  Prisms  (110)  and  Brachy-Domes  (Oil). 
Aragonite 149,  150, 153 

Fig.  552.  Orthorhombic.  A  Penetration  Twin  produced 
by  the  interpenetration  of  two  crystals  showing  the 
planes  of  Prisms  (110),  Brachy-Pinacoids  (010)  and  Basal- 
Pinacoids  (001).  Staurolite 149, 150,  153 

Fig.  563.  Orthorhombic.  A  Penetration  Twin  showing  the 
planes  of  Pyramids  (111),  Prismatic  Planes  (110),Brachy- 
Dome  Planes  (021,  012)  and  Brachy-Pinacoids  (010). 
Cerussite 149, 150,  153 

Fig.  554.  Orthorhombic.  A  Penetration  Twin  formed  by 
the  interpenetration  of  two  crystals  showing  the  planes  of 
Brachy-Pinacoids  (010),  Basal-Pinacoids  (001),. Brachy- 
Domes  (Oil),  and  Prisms  (110).  Staurolite  .  .  .  149,  150, 153 

Fig.  555.  Orthorhombic.  A  Penetration  Twin  produced 
by  the  interpenetration  of  three  crystals.  This  form  is 
known  as  a  Trilling.  It  exhibits  the  planes  of  Basal- 
Pinacoids  (001),  Brachy-Pinacoids  (010),  Prisms  (110) 
and  Macro-Domes  (101).  Staurolite 149,  150, 153 

Fig.  556.  Orthorhombic.  Similar  to  Fig.  555.  Staurolite, 

149, 150, 153 

Figs.  557,  558,  559.  Orthorhombic.  Figures  illustrating 
the  building  up  of  penetration  twins  in  such  a  manner  as 
to  produce  a  pseudo-hexagonal  form  as  outlined  in  Fig. 
559  or  a  case  of  Mimicry 149, 150, 154 

Fig.  560.  Orthorhombic.  A  Twin  form  or  an  imperfect 
Fiveling  roughly  simulating  a  hexagonal  form.  Marca- 
site 149, 150,  154 

Fig.  561.  Orthorhombic.  Mimicry.  Section  of  the  top  of 
a  twinned  form  similar  to  Fig.  564,  showing  a  resemblance 
to  a  hexagonal  form,  but  the  twinning  is  indicated  by  the 
re-entering  angles.  Aragonite 149, 150, 154 


DESCRIPTIONS    OF    THE    PLATES.  257 

PAGE 

Fig.  562.  Orthorhombic.  A  Twin  Form  of  a  Fiveling 
type,  roughly  simulating  a  hexagonal  form.  Marcasite, 

149, 154 

Fig.  563.  Orthorhombic.  A  Contact  Twin  showing  the 
planes  of  Prisms  (110),  Macro-Pinacoids  (100),  and 
formed  by  revolving  one  part  of  the  crystal  for  180° 
about  the  plane  (abcdef).  This  form  shows  the  com- 
mencement of  Mimicry  that  leads  to  the  production  of  a 
pseudo-hexagonal  form  as  seen  in  Figs.  551,  564,  559, 
561  and  580.  Aragonite 149,  150,  154 

Fig.  564.  Orthorhombic.  A  Combination  Twin  forming  a 
pseudo-hexagonal  form  produced  by  repeated  twinning. 
Mimicry.  Aragonite 149, 150, 154 

Fig.  565.  Orthorhombic.  A  Penetration  Twin  showing  the 
planes  of  Prisms  (110)  and  Pyramids  (111),  making  a  form 
roughly  simulating  the  hexagonal  forms.  Mimicry  com- 
pleted in  Fig.  566.  Cerussite 149, 150, 154 

Fig.  566.  Orthorhombic.  A  Penetration  Twin  produced 
by  the  complete  twinning  of  Fig.  565,  so  as  to  fill  out  the 
re-entering  angles.  Complete  Mimicry  of  the  Hexagonal 
Pyramid.  Cerussite 149, 154 

Fig.  567.  Orthorhombic.  A  Penetration  Twin  or  Trilling, 
simulating  a  Hexagonal  Crystal.  Mimicry.  Chryso- 
beryl 149,  150, 154 

Fig.  568.  Orthorhombic.  Mimicry.  Repeated  twinning 
producing  a  pseudo-Hexagonal  Pyramid.  Bromelite, 

149, 164 

Fig.  569.  Orthorhombic.  Mimicry.  A  cross  section  of 
Fig.  568.  The  lines  with  looped  ends  show  the  position 
of  the  optic  axes  in  the  different  individuals  composing 
the  pseudo-hexagonal  form.  Bromelite 149,  154 

Figs.  570,  571,  572,  573,  574.  Monoelinic.  Mimicry.  These 
figures  illustrate  successive  stages  in  twinning,  simulating 
Orthorhombic,  Tetragonal,  and  Isometric  Forms.  Fig. 


258  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

574  is  so  twinned  that  if  it  were  not  for  the  obtuseness  of 
the  facial  angles  it  would  simulate  the  Hexakis  Octa- 
hedron, but  as  it  occurs  it  closely  mimics  the  Dodeca- 
hedron. Phillipsite 149. 150, 154 

Figs.  575, 576, 577, 578, 579.  Orthorhombic.  Mimicry.  Sim- 
ulating hexagonal  forms.  Fig.  579  is  a  cross  section  of 
one  of  them  in  which  the  optic  axes  are  shown  by  lines 
with  looped  ends.  Witherite 149, 154 

Fig.  580.  Orthorhombic.  Mimicry.  A  cross  section  of  a 
twin  like  Fig.  564,  taken  approximately  midway  between 
the  two  ends.  The  striations  show  the  different  indi- 
viduals of  which  it  is  composed,  while  the  slightly  re- 
entering  angles  indicate  the  twinning.  Aragonite  .  .  •  154 

PLATE  XXIV 

Fig.  581.  Triclinic.  Holohedral.  This  shows  by  its  central 
ring  that  it  has  a  Center  of  Symmetry.  The  dotted 
straight  lines  with  feathered  ends  show  that  the  Crystal- 
lographic  Axes  are  not  Axes  of  Symmetry.  The  dotted 
circle  indicates  that  there  is  no  Plane  of  Symmetry.  The 
figure  indicates  that  the  Triclinic  System  has  neither 
Plane  nor  Axis  of  Symmetry  but  that  it  has  a  Center  of 

Symmetry 161, 162, 168 

The  Triclinic  Hemihedral  or  Asymmetric  is  shown  in 
Fig.  608 167, 168 

Fig.  582.  Monoclinic.  Holohedral.  This  figure  shows  that 
the  Holohedral  Monoclinic  crystals  have  a  Center  of  Sym- 
metry, an  Axis  of  Binary  Symmetry  and  a  Plane  of  Sym- 
metry   161, 162, 170 

Fig.  583.   Monoclinic.    Hemihedral  or  Clinohedral.    One 

Plane  of  Symmetry  only 161,162,169 

The  Monoclinic  Hemimorphic  is  shown  in  Fig.  609, 
page  169. 


DESCRIPTIONS   OF   THE   PLATES.  259 

PAGE 

Fig.  584.  Orthorhombic.  Holohedral.  The  figure  shows  a 
Center  of  Symmetry,  three  Axes  of  Binary  Symmetry  and 
three  Planes  of  Symmetry •>'••'•'.  .161,162,170 

Fig.  585.  Orthorhombic.  Hemihedral.  The  figure  has 
three  Axes  of  Binary  Symmetry  only  ......  161-163, 170 

Fig.  586.  Orthorhombic.  Hemimorphic.  The  figure  shows 
one  Axis  of  Binary  Symmetry  and  two  Planes  of  Sym- 
metry .  ,  .  . ...*,.  .  .  161-163,  170 

Fig.  587.  Tetragonal.  Holohedral.  This  figure  shows  a 
Center  of  Symmetry,  four  Axes  of  Binary  Symmetry,  one 
Axis  of  Tetragonal  Symmetry,  and  five  Planes  of  Sym- 
metry   161-163, 175 

Fig.  588.  Tetragonal.  Sphenoidal.  This  figure  has  three 
Axes  of  Binary  Symmetry  and  two  Planes  of  Symmetry, 

161-163, 174 

Fig.  589.  Tetragonal.  Pyramidal.  This  figure  has  a  Center 
of  Symmetry,  an  Axis  of  Tetragonal  Symmetry,  and  a 
Plane  of  Symmetry 161-163, 174 

Fig.  590.  Tetragonal.  Trapezohedral.  This  figure  has  four 
Axes  of  Binary  Symmetry  and  one  Axis  of  Tetragonal 

Symmetry  only 161-163, 174 

The  Tetragonal  Bisphenoidal  or  Tetartohedral  is  shown 
in  Fig.  610,  page  172;  the  Tetragonal  Pyramidal  or  Hemi- 
morphic is  illustrated  in  Fig.  611,  pages  172, 173,  and  the 
Ditetragonal  Pyramidal  or  Hemimorphic  is  exhibited  in 
Fig.  612,  page  175. 

Fig.  591.  Hexagonal.  Holohedral.  This  figure  shows  a 
Center  of  Symmetry,  six  Axes  of  Binary  Symmetry,  one 
Axis  of  Hexagonal  Symmetry  and  seven  Planes  of  Sym- 
metry   ...  ....  161-163, 182 

Fig.  592.  Hexagonal.  Hemihedral.  Khombohedral.  This 
figure  shows  a  Center  of  Symmetry,  three  Axes  of  Binary 
Symmetry,  one  Axis  of  Trigonal  Symmetry,  and  three 
Planes  of  Symmetry .161,162,164,179 


260  DESCRIPTIONS    OF    THE    PLATES. 

PAGE 

Fig.  593.  Hexagonal.  Pyramidal.  Hemihedral.  The  fig- 
ure exhibits  a  Center  of  Symmetry,  one  Axis  of  Hex- 
agonal Symmetry,  and  one  Plane  of  Symmetry, 

161, 162, 164, 181 

Fig.  594.  Hexagonal.  Hemihedral.  Trapezohedral.  This 
figure  shows  six  Axes  of  Binary  Symmetry  and  one  Axis 
of  Hexagonal  Symmetry 161,162,164,181 

Fig.  595.  Hexagonal.  Hemihedral.  Trigonal.  This  fig- 
ure shows  a  Center  of  Symmetry,  three  Axes  of  Binary 
Symmetry,  one  Axis  of  Trigonal  Symmetry,  and  four 
Planes  of  Symmetry 161,162,164,180 

PLATE  XXY 

Fig.  596.  Hexagonal.  Tetartohedral.  Rhombohedral.  This 
figure  exhibits  a  Center  of  Symmetry  and  one  Axis  of  Tri- 
gonal Symmetry  only  . 161,162,164,177 

Fig.  597.  Hexagonal.  Tetartohedral.  Trapezohedral.  This 
figure  shows  three  Axes  of  Binary  Symmetry  and  an  Axis 
of  Trigonal  Symmetry 161,  162, 164, 177 

Fig.  598.  Hexagonal.  Tetartohedtal.  Trigonal.  This  fig- 
ure shows  an  Axis  of  Trigonal  Symmetry  and  a  Plane  of 
Symmetry 161, 162, 165, 178 

Fig.  599.  Hexagonal.  Hemimorphic.  lodyrite  Type.  This 
Type  has  an  Axis  of  Hexagonal  Symmetry  and  six  Planes 
of  Symmetry 161, 162, 165, 182 

Fig.  600.  Hexagonal.  Hemimorphic.  Neph elite  Type.  This 
Type  possesses  an  Axis  of  Hexagonal  Symmetry  only, 

161,  162,  165,  178 

Fig.  601.  Hexagonal  Hemimorphic.  Tourmaline  Type.  This 
Type  has  an  Axis  of  Trigonal  Symmetry  and  three  Planes 
of  Symmetry 161,  162, 165,  178 

Fig.  602.  Hexagonal.  Hemimorphic.  Sodium  Periodate 
Type.  This  Type  possesses  an  Axis  of  Trigonal  Sym- 
metry only  161,162,165,176 


DESCRIPTIONS    OF    THE    PLATES.  261 

PAGE 

Fig.  603.  Isometric.  Holohedral.  This  figure  shows  a  Cen- 
ter of  Symmetry,  six  Axes  of  Binary  Symmetry,  four  Axes 
of  Trigonal  Symmetry,  three  Axes  of  Tetragonal  Sym- 
metry, and  nine  Planes  of  Symmetry  .  .  .  .161, 162, 165, 186 

Fig.  604.  Isometric.  Hemihedral.  Oblique.  This  figure 
indicates  three  Axes  of  Binary  Symmetry,  four  Axes  of 
Trigonal  Symmetry,  and  four  Planes  of  Symmetry, 

161,  162,  165, 185 

Fig.  605.  Isometric.  Hemihedral.  Parallel.  This  figure 
shows  a  Center  of  Symmetry,  three  Axes*of  Binary  Sym- 
metry, four  Axes  of  Trigonal  Symmetry,  and  three  Planes 
of  Symmetry 161,  162, 166, 184 

Fig.  606.  Isometric.  Hemihedral.  Gyroidal.  These  forms 
possess  six  Axes  of  Binary  Symmetry,  four  Axes  of  Tri- 
gonal Symmetry,  and  three  Axes  of  Tetragonal  Sym- 
metry  161,162,166,184 

Fig.  607.  Isometric.  Tetartohedral.  This  figure  has  three 
Axes  of  Binary  Symmetry,  and  four  Axes  of  Trigonal 
Symmetry  only 161,162,166,183 

Fig.  608.  Triclinic.  Asymmetric.  This  figure,  as  its  name 
implies,  is  destitute  of  symmetry 161,  162, 168 

Fig.  609.  Monoclinic.  Sphenoidal  or  Hemimorphic.  This 
figure  has  one  Axis  of  Binary  Symmetry  only  .  .161, 162, 169 

Fig.  610.  Tetragonal.  Bisphenoidal  or  Tetartohedral.  This 
figure  has  one  Axis  of  Binary  Symmetry  only  .  .161, 162, 173 

Fig.  611.  Tetragonal.  Pyramidal.  Hemimorphic.  This 
figure  possesses  one  Axis  of  Tetragonal  Symmetry  only, 

161, 162, 173 

Fig.  612.  Ditetragonal.  Pyramidal.  Hemimorphic.  This 
figure  has  one  Axis  of  Tetragonal  Symmetry  and  four 
Planes  of  Symmetry -.;  ..  .  ..:.  ..  .  .161,162,175 


EKEATA. 

Page  7.      7  lines  from  the  top.      For  "A  B  C  D  E  F  H" 

read  "A  B  C  It." 

Page  11.     2  lines  from  the  bottom.     For  "001"  read  "001." 
Page  12.     13   lines  from  the  top.     For  "110    <   111"  read 

"Oil  <  Oil." 

Page  21.     8  lines  from  the  top.     For  ' '  equal ' '  read  ' '  unequal. ' ' 
Page  26.     7  lines  from  the  top.     For  "35"  read  "64." 
Page  32.     2  lines  from  the  bottom.     For  "P"  read  "P." 
Page  33.     5  lines  from  the  top.     For  '"P»  read  "'P." 
Page  35.     6  lines  from  the  bottom.     For  "n&"  read  "—  nb." 
Page  35.     2  lines  from  the  bottom.     For  "  &  "  read  "  —  6. " 
Page  41.     12  lines   from  the  bottom.     Strike  out   "shortest" 

and  for  ' '  them '  >  read  < '  their  centers. ; ' 

Page  43.     11  lines  from  the  top.     For  "65,   70"  read  "67, 

68."     10  lines  from  the  bottom  for  "82-86"  read  "82,  84-86." 
Page    45.     12    lines    from    the    bottom.     For    "65    72"    read 

"65-72." 

Page  47.     2  lines  from  the  top.     For  the  second  b  read  &. 

Page  54.  9  lines  from  the  top.  For  "Ortho"  read  "Macro," 
10  lines  from  the  top.  For  "  ortho-"  read  "macro-."  11  lines 
from  the  bottom.  For  "clino-"  read  "brachy-"  and  for 
"  Clino-"  read  "  Brachy-."  10  lines  from  the  bottom.  For 
' '  ortho- ' '  read  ' '  macro-. ; '  9  lines  from  the  bottom  for 
"Ortho-"  read  « Brachy-." 

Page  57.    13  lines  from  the  top.    For  "  87  135  "  read  ' ' 87-135. ' ; 

Page  60.  .2  lines  from  the  bottom.  For  ' '  147-149 ' '  read  ' '  151- 
153." 

Page  61.  6  lines  from  the  top.  For  "  147,  150  and  "  read 
"151-  .' 

(262) 


Page  83.  7  lines  from  the  bottom  for  "(d)77  read  "  (s)  77 
and  for  "  (b  and  g)  77  read  "  (b  and  d).77 

Page  125.  14  lines  from  the  top.  For  "Petagonal77  read 
"Pentagonal.7' 

Page  132.  4  and  7  lines  from  the  bottom.  Place  "upper77 
before  "edge.77 

Page  133.  10  lines  from  the  bottom.  Place  "upper77  before 
"  edge.77  7  lines  from  the  bottom  for  "  845  77  read  "  345. 77 
3  lines  from  the  bottom.  Tor  " octohedral 7 7  read  "octahedral.77 

Page  134.  7  lines  from  the  top.  Place  "upper77  before 
"edge.77 

Page  140.  10  lines  from  the  bottom.  For  "alteration77  read 
'  *  alternation. 7  7 

Page  144.  14  lines  from  the  top.  For  "  four  77  read  "  five.77 
6  lines  from  the  bottom  add:  "  if  the  planes  are  pentagonal;  but 
if  they  are  triangular  they  belong  to  the  Kexakis  Tetrahedron. 

Page  147.     9  lines  from  the  top.     For  "llch"  read  "Ikh." 

Page  151.  3  lines  from  the  top.  For  "  459-460 77  read  "459, 
460. 77 

Page  157.     11  lines  from  the  top.     For  "10177  read  "101.77 

Page   169.     Last  line.     For  "4877  read  "45.77 

(263) 


Pte 


Fig.  I 


-b 


-  z 


Monoclinic 

Plane  of  Symmetry 

Axis  of  Binary  Symmetry 


Triclinic  Axes 


Fig.  4 


-t-x 


+Y 


-  fetratbnal  Ares 


-0    -X 


- 


Isometric  Axes 


Fig.  2 


-b 


r*Y 


Fig.  3 


t- 

-y 


Monoclinic  Axes 


noclinic 

ne  of  Symmetry 

s  of  Binary  Symmetry 


Fig.  6 


t  c 


a 


a 


Hexagonal  Axes 


-a 


-t 


Fig.  II 


-y 

Orthorhombic 
Axes 


Fig.9 


Monoclinic 
Plane  of  'Symmetry 
Axis  of  Binary  Symmetry 


Monoclinic 
Plane  of  Symmetry 


Fig.  12 


Fig.  1 3 


Isometric 
Distorted  Oclahdrons 


Fig.  18 


no 


110 


III 


Fig.  1 9 


Isometric 
Distorted  Octahedrons 


Fig.   20 


Isometric 
Curved  Octahedron 


Fig.  2  4 


Isometric 
Parallel  Growths 


Fig.  25 


Fig.  26 


Tetragonal 
Parallel  Growths 


Hexagonal  Parallel  Growths 

Fig.  3 1  Fig.  32 


Hexagonal 
Parallel  Growths 


II 


Fig.  21 


Hexagonal 
Distorted  Form 


Fig.  28 


Fig.  id 

001 


Fig.  I  7 


Orthorhombic 
Distorted  Crystal 


Isometric  Octahedron 
Modified 


Fig.  23 


Insometric 
Parallel  Growths 


Fig.  3o 


Fig.  3  5 


PM1 


\ 


Nix  / 


oo-Poo 

100 


no 


Fig.36  Fig.37 


101 


1010 

OCtP 


000 


Hexagonal 


Triclinic 
Center  of  Symmetry 


Hexagonal 


Tetragonal  System 


Hexagonal 


Axf 


Axes  of  Tetragonal  Symmetry 


FigJ* 


Fig. 5  ^ 


021 


101 


IOO 


00  P 

no 


201 


Hexagonal 
Axes  of  Trigonal 

SkmmaieL 


Orthorhombic 

three  Planes  of 

Symmetry 


Isometric 
Pentagonal  Dodecahedrons 

.1  ' '  •  'v      '  / 

'n 


Fig.  40 


Hexagonal 


Fig.  41 


110 


Hexaaonal 


Hexagonal 

Symmetry 


Fig.  46 


Tetragonal 

Axis  of  Tetragonal 

Symmetry 


Fig.  4  8 


Hexagonal 

f  Trigonal  Symmetry 


Hexagonal 

Trigonal  Trapezohedrons 


Three  Planes  of  Symmetry 


Fig.  58 


Pla 


f^"                OOT                            ^^^ 

f^     f  T0  «o     3o/ 

b 

d 

a 

|0                      ec,  0~> 

oio 

/oo 

* 

I  —  I 

i& 

Isometric 


Isometric 


Fig Jb  2 

J^Fig 

7/o  /      '      /      '     ^AP- 


'-^/^ 

c?/c?  /  /y0 
:u....L..L.^_ 


Fig.   88 


O2T 

Orthorhombic 

Fig.  io  3 


teV 


Fig.  89 

TQI    POO 


OP 

^-001.  -- 


s 


IOI 


Fig.  90 

TOI    Poo  ^ 

oP 
•v  -QPJ__ 


IOI 


.0 


F 


Orthorhombic 


i>.  95 


Orthorhombic 


Fig.Tl-3 


Orthorhom 

Fig.  II 9        Fig.  1 20 


Orthorhombic    Fig.  135 


.    .  ,        Isometric  DyaKis 
pAsr^        Dodecahedrons 


nrthnrhnmbic  Suhenoids 


Fig'i4d         Fig.i47 


Fig 


Fig.l5i 


Orthorhom 

Fig.  153 


no 


no 


-L^ 


\ 

\ 

i 

-IP 

1 

L 

-F-! 

-p 

no 

iod 

no 

1 

i 

i 

I- 

i 



Primary  Prism 

Fig.i57 


Primary  and  Secondary  Prisms 


K^ 

fifc^p 

-p 

* 

9 

o 

IOO 

no 

M 

0 

& 

0 

J  

J 

Tetragonal  Prisms  and 
Pyramids 


Cross  Section  of  a 
Secondary  Prism 


Tetragonal  Pyramids 


Fig- HP 


Fig.  172 


Pli 


Tetragonal 
Pyramid  and 
Basal  Planes 


Pyramid  and  Prism 

Fig.  1 80 


Sonenoid 


Fig.177 


Fig.  199 

Fig.  200 


Tetragonal 
Scheelite 


Cross  Section 


lodyriU  Type 


Fig.  203 


r 

«, 
8 

u 

— 

u  c 

T— 

)\  

oop 

;-> 

10 

c 

v 

OIT 

0 

. 
i 

-• 

1 

Primary 
Hexagonal  Pyramid 


Secondary  Hexagonal 
Pyramid 


Fig.2IO 


Fig.  205 

Primary  Hexagonal 
Prism 

Fig.2II 


1122 

Pyramidal  Relations 


Fig.2i8 


Fig- 2  20 


Fig.2i7 


ephelite 
Type 


10  Cross  Section 

Dihexagonal  Pyrami4 


KT(|I20) 


Oo  P  2 

4 


Secondary  Trigonal -Prism 

Fig.  2  27     Fig.  *  28        Fig. 


Rhombohedrons 


Fig.235 


Fig.239      F'Z~ 23 


Ft?  237  A     Dihexa9°nal 

*      ^7    A         Pyramid 


Pyramids 


Pyramids 


Tetrannnal 


Hexagonal         Pyramids 


ig.263 

Hexagonal         Pyramids 


\/Fig267  Fig. 2  69 


•Ftg.277^^ 

^W^ 

ASAWt        pi      ?8 


— ~«. 
Rhombohedrons 

Fig.279 


Scalenohedrons 


X/7 


Hexagonal        y     Scalenohedrons 


Fig- 298 


Fig.  300 


Fig.  30 1 


7ZP 


Hexagonal 
Compound  Form 


^z'oii  JP\ 

rS^\ 

202  O   . 

ooP 

ooP 

^2* 

Hexagonal 


Fig.3Q2 


Fig-304 


Fig. 3 '20 


Fig.  32 1 


Fig.  322 


00  |P, 

1126 


oo  P 

roTo 


Fig  326 


Diitexagonal  Pyramid 


Fig.  330 


Hexagonal  Compound   Forms 

Fig. 327 


Periodate  Type       . 


Fig.334 


Hexakis  Octahdrons 


IOO 


Fig.  325 


Hexahedron  or 
Cube 


Dodecahedron 


Fig-332 


Fig.333 


Tetrahdron 


Fig.34i 


Fig.  34  2     JDr; 


Tetrahedrons 

Flg.346       Fig.  3  47 


Trigonal  Tria 
Octahedror 


Fig.  3  48 


Pentagonal  s 

Dodecahedron        l\1  h  k  I  \ 


Dyakis 


^iv.363 


Pentagonal 

FiS-  364^T^~J^  Fig.365 


Dodecahedrons 


Hexakis 
Octahedron 


Fig.  366 


Dlak 


Fig.  367 


Fig.3  68 


mOn 


Pentagonal      y 

Fig.  372 


Icositetrahedrons 


Fig.  37 3 


QQ000 

IOO 


Cube  modified  by  an  Octahedron 


Octahedron  modi 
a  Cube 


Fig-376 


F'g-377 


no 


IOO 


.A     >• 


X_ 


Dodecahedron  modified  by  a 
Cube 


Cube  and  Dodecahedron 


Fig.382 


Fig.  38o 


ooOoo 

IOO 


Fig.38l 


!ioo 


Modified  Cubes 


F'g.  369  Fig.370 

Ff  ^ — ^  *fr 


o 

Oo0ao 
III 

Tetrahedral  Pentagonal  Dodecahedron  IOO 

Fig- 374  Fi*  375 


Cube  modified  by 
an  Octahedron 


nedron  modified 
>y  a  Cube 


Fig,  378 


Cubo-Octahedron 

Fig.  379 


Octahedron  and  Dodecahedron 

Fig.  383  pig.  384 


Dodecahedron 
and  Octahedron 


Fig.  385 


Modified 

lodecahedron 


Modified 
Cube 


Modified 
Dodecahedron 


Fig.4i6 


Fig.  446 


oo  0  oo         jQO 


Parallel  Growths 


oo          I  O  O 
Om      7l{hko} 


Fig.463 


Twinning 


Fig  462 


Polysynthetic  Twinning 


d 


Octahedron 


Fig.467 


Fig.468 


Fig.  469 


00  </  00 


XIX 

Fig.452 


100          Fig  454 


Fig-455 


Fig  4-53 


Growths 


oo«/oc         IOO 

-»»*<**,}      sstS& 


Fig  46o 


roo 
7T{AM 

F*>  467 


Polysynthetic 
Twinning 


Polysynthetic 
Twinning 


Fig  4  64 


Polysynthetic  Twinning 

»•*  ^ 

Fig.  465  Fig- 46  6 


Contact 
Twin 


Octahedron 


Contact 
Twin 


Fig.  470 


Fig.  471 


Fig.  472 


Fig.473, 


Fig.  41 '8 
Fig.483         Fig.484        Fig.485 


Pic. 


\x<* 

1 

/:\ 

/: 

\    *^ 

f 

\ 

/ 

b 

,p 

00 

A. 

P 

0 

1 

?y 

no 

^ 

-4 

..... 

•• 

I'OJJ 

•p 

\   / 

X>\    ' 

c 

^^ 

Fig.501 
Fig.507 


teXXI 


Plate 


Fig.525 


are 


I*/// 


Plate 


Conventional 
Signs  for  Axes                            /' 
of  Symmetry 

/^ 

V  / 

^ 

|        Bjnar>                                                           .---'\L 

^      Trigonal                                     "0t''~'~ 

5  —  U-'-""'3 

*r 

^     Tetragona                                        \ 

0       Hexagonal                                           xxx 

/          \ 

x                               N. 

O     Center  of                                                            ~~', 
Symmetry 

Fig 

r"          ^r^ 

5^/                  F/^.552 

Triclinic                                            Monoclinic 

\ 

\ 
\ 

\ 

V 

/ 

Orthorhombic 

Hemimorphic 


Fig.  58  7 

Tetragonal 
Holohedral 


Fig.  5 9° 


Tetragonal 
Trapezohedral 


Fig.5?i 


Hexagonal 
Holohedral 


Hexagonal 
Hemihedral 
Rhombohedral 


iXIV 


"*-... 


Fig.588 


Tetragonal 
Sphenoidal 


Fig-5%9 


Tetragonal 
Pyramidal 


Fig.593 


Hexagonal 

Hemihedral 

Pyramidal 


Fig.594 


Hexagonal 

Hemihedral 

Traoezohedral 


Fig.595 


Hexagonal 

Hemihedral 

Trigonal 


Fig.  596 


Fig.597 

JL 


V 


Hexagonal 
Tetartohedral 
Rhombohedral 


Hexagonal 
Tetartohedral 
Trapezohedral 


Hexagonal 

Tetartohedral 

Trigonal 


Fig.  602 


Fig.  60 3 


Hexagonal 

Hemimorphic 

Socfium  Periodate  Type 


Isometric 
Holohedral 


Fig  ^6  08 


Fig -60  7 


V         Fig.609 


x 


IX  V 


Fig.  599 


Fig-  600 


Fig.  ()O  l 


\      '    ^ 


Hexagonal 

Hemimorphic 
lodyrite  Type 


Hexagonal 
Hemimorphic 
Nephelite  type 


Fig-  ^605 


Hexagonal 

Hemimorphic 

Tourmaline  Type 


Fig.  606 


Tetragonal 

Pyramidal 

Hemimorphic 


\ 


Tetragonal 

Bisphenoidal  or 


INDEX. 


Acute  Bhombohedron,  87 
Adamantoid,  124,  130,  137,  144, 

186,   188,  201,   207,   236-239, 

241,  242 
Agassiz,  Louis  Jean  Budolphe, 

188 
Aggregate,    Mineral,    149,    150, 

247 
Albite,  12,  13,  19-21,  25,  26,  33, 

34,  44,  149,  150,  152,  205,  249 
Alum,  3,  149 

Amorphous  Minerals,  148 
Angles,  Axial,  7,  8,  9,  40,  50,  73 
Angles  of  the  Hexagonal  Scale- 

nohedron,    89 
Angles,  Ehombohedral,  86 
Angles,    Variation    of    Crystal 

angles,  3 

Animal  Kingdom,  1 
Anorthoid,  193 
Anorthotype,  193 
Apatite,  18,  26,   74,  76,   80-83, 

104,  206,  234 

Apophyllite,  61,  70,  73,  74 
Aragonite,   149,   150,  153,   154, 

247,  250,  256-258 
Asymmetric  Class,  167,  261 
Asymmetric  Class,  Symmetry  of, 

168,  261 

Asymmetric  Group,  167,  261 
Augite,    17,   18,    26,    41,   43-47, 

149,  150,  152,  203,  209,  249 
Augitoid,  193 


Axenite,  12,  13,  19-21,  25,  26, 

33,  34,  44,  205 
Axes,  Crystal,  6-10 
Axes,  Crystallographic,  how  rep- 
resented, 161 
Axes,  Cubic,  131,  139 
Axes,  Dodecahedral,  131,  139 
Axes,  Hexagonal,  8,  73,  75,  109, 

203 

Axes,  Octahedral,  131,  135,  139 
Axes  of  Symmetry,  18,  19,  23- 

25,  41 

Axes  of  Symmetry,  how  repre- 
sented, 161,  162 
Axes  of  the  Isometric  System, 

7,   122,  126,  203 
Axis    of    Trigonal    Symmetry, 

how  represented,  162 
Axes,   Orthorhombic,  7,  50,  57, 

203 
Axes,  Monoclinic,   7,  40-42,  47, 

203 
Axes,    relation    to    Planes,    43, 

51,  62 
Axes,     relation    to     Hexagonal 

Planes,  75 

Axes,  Tetragonal,  7,  60,  203 
Axes,    Triclinic,    7,    9,    10,    29, 

33,  203 

Axial  Angles,  7,  8,  9,  40,  50,  73 
Axial  Models,  13 
Axis  of  Binary  Symmetry,   18, 

19,   23-25,  41,  44,  51-56,   64, 


(265) 


266 


INDEX. 


67,  69,  84,  90,  91,  94,  96, 
100,  123,  131,  135,  138,  139, 
141,  162-166,  258-261 

Axis  of  Binary  Symmetry,  how 
represented,  162 

Axis  or  Hexagonal  Symmetry, 
18,  19,  41,  74,  76,  85,  93,  94, 
103,  121,  163-165,  259,  260 

Axis  of  Tetragonal  Symmetry, 
18,  19,  ^3,  41,  64,  68,  69,  123, 
130,  131,  139,  163,  165,  166, 
259,  261 

A.XIS  of  Trigonal  Symmetry,  19, 

.  23-25,  41,  52,  74,  76,  85,  91, 
96,  98,  100,  102,  103,  104, 
121,  130,  135,  138,  139,  141, 
164-166,  259-261 

Axis,  Twinning,  152 

Axis,  Vertical,  10,  41 

Barite,  26,  50,  51,  57,  207,  212 
Basal  Cleavage,  155-158 
Basal  Pinacoid,  11,  21,  42,  44, 

60,  63,  80,  104,  172-183,  199 
Basal  Pinacoid,  Hexagonal,  176- 

183 
Basal  Plane,  11,  21,  42,  44,  60, 

63,  80,  104,  172-183,  199 
Base,  199 

Bauerman,  H.,  x,  34 
Beryl,  74,  76,  80,  83,  104 
Berylloid,  197 
Bevelment,  27,  28 
Binary    Symmetry    Axis,    how 

represented,  162 
Binomial  Names,  188 
Biology,  1 
Bi  Pyramid,  197 
Bipyramidal  Class,  181,  182 
Bipyramidal  Class,   Orthorhom- 

bic,  171,  172,  259 


Bipyramidal  Class,  Tetragonal, 

174,   175,   261 
Bisphenoidal  Class,  Tetragonal, 

172 

Black  Douglas,  188 
Black  Hexagon,  162 
Black  Quadrilateral,  162 
Black     Spindle-shaped    Figure, 

162 

Black  Triangle,  162 
Bohemia,  187 
Botany,  1 
Boracitoid,  201 
Borax,  41,  43-47,  210 
Brachy-Axis,  10 
Brachy-Diagonal,  10 
Brachy  Diagonal  Dome,  190 
Brachy  Diagonal  Pinacoid,  200 
Brachy  Diagonal  Prism,   190 
Brachy-Dome,  12,  22,  54,  190 
Brachy-Pinacoid,  3,  12,  21,  54, 

200 
Brachy-Pinacoidal         Cleavage, 

155-157 

Brachy-Semi-Axis,  50 
Bravais,  C.,  29,  167 
Bromelite,  149,  154,  257 
Brush  and  Penfield's  Manual,  x 

Calamine,  51,  57,  212 

Calcite,  18,  27,  74,  76,  81,  83, 
87-89,  104,  149,  150,  152,  207, 
223,  231,  234,  249-252 

Calcite  Pyramid,  197 

Cassiterite,  61,  62,  70,  73,  74, 
149,  150,  152,  153,  220,  251, 
252 

Center  of  Symmetry,  19,  23-25, 
55,  56,  59,  64,  67,  68,  72,  85, 
91,  93,  98,  100,  121,  131,  135, 
139,  141,  147,  162-166,  258- 
261 


INDEX. 


267 


Center  of  Symmetry,  how  rep-   ' 

resented,  162 
Centrosymmetric      Class,      168, 

205,  206,  258 
Cerussite,    149,    150,    153,    154,   | 

256,  257 
Chabazite,    149,   150,    153,   253,  ! 

255 
Chalcanthite,  12,  13,  19-21,  26,  ; 

33,  34,  44,  205 
Chalcopyrite,  149,  150,  192,  153,  j 

253 
Characteristics     of     Hexagonal 

Crystals,  76 
Characteristics      of      Isometric 

Crystals,  123 
Characteristics     of     Monoclinie 

Crystals,  44 
Characteristics  of  Orthorhombic 

Crystals,  53,  54 
Characteristics     of     Tetragonal 

Crystals,  62 

Characteristics       of       Triclinic 
Crystals,  19-21 
Chrome  Alum,  3,  14,  26,  204 
Chrysoberyl,  149,  150,  154, 
Class   of    the    Dihexagonal    Bi- 

pyramid,  182,  183 
Class  of  Dihexagonal  Pyramid, 

182,  183 

Class  of  the  Diploid,  184,  185 
Class   of   the  Ditetragonal  Bi- 

pyramid,  175,  176 
Class  of  the  Ditetragonal  Pyra- 
mid, 175 
Class  of  the  Ditrigonal  Bipyra- 

mid,  180 

Class   of  the   Ditrigonal  Pyra- 
mid, 178-180 
Class  of  the  D^crigonal  Scale- 

nohedron,  179 


Class  of  the  Gyroid,  184 
Class   of  the  Hemimorphic   Di- 
hexagonal Pyramid,  182 
Class  of  the  Hemimorphic  Tri- 
gonal Pyramid  of  the  Third 
Order,  176,  177 
Class  of  the  Hexagonal  Trape- 

zohedron,  181 
Class    of    the    Hextetrahedron, 

185,  186 
Class  of  the  Rhombohedron  of 

the  Third  Order,  177 
Class  of  the  Tetartoid,  183,  184 
Class   of  the  Tetragonal  Pyra- 
mid of  the  Third  Order,  172, 
173 

ulass  of  the  Third  Order  Hexa- 
gonal Bipyramid,  181,  182 
Class  of  the  Third  Order  Hexa- 
gonal Pyramid,  180-182 
Class   of  the   Trigonal   Bipyra- 
mid of  the  Third  Order,  178 
Class  of  the  Trigonal  Pyramid 

of  the  Third  Order,  178 
Class  of  the  Trigonal  Trapezo- 

hedron,  177,  178 
Cleavage,  Cubical,  155,  159 
Cleavage     Dodecahedral,      155, 

159 

Cleavage,  Hexagonal,  158 
Cleavage,  Isometric,  159 
Cleavage,  Mineral,  155-160 
Cleavage,  Monoclinie,  157 
Cleavage,  Octahedral,  155,  159 
Cleavage,  Orthorhombie,  157 
Cleavage,    Pinacoidal,    155-158 
Cleavage  Plate,  155 
Cleavage,  Prismatic,  155-158 
Cleavage,  Pyramidal,  155-158 
Cleavage,     Rhombohedral,    155, 
158 


268 


INDEX. 


Cleavage  Shorthand,  156-159 
Cleavage,  Slaty  or  Rock,  160 
Cleavage,  Tetragonal,  157,  158 
Cleavage,  Triclinic,  156 
Clino-Axis,  42 
Clino-Diagonal,   42 
Clino-Diagonal  Prism,  190 
Clino-Dome,  43,  44,  190,  203 
Clinohedral  Group,  46,  169,  170, 

258 

Clinohedrite,  46 

Clinorhombic    Octahedron,    193 
Clino-Pinacoid,  8,  11,  12,  17,  18, 

26,  41,  43,  44,  46,  47,  200,  203 
Clino-Pinacoidal  Cleavage,  155- 

157 

Colby  University,  vi 
Composition    Plane,    152,    247- 

253,  257 

Compound  Crystals,  25,  26 
Compound     Forms,     Hexagonal 

System,  104 
Compound      Isometric      Forms, 

141,  142 

Compound    Minerals    or    Crys- 
tals, 149-154 

Compound  Monoclinic  Forms,  46 
Compound  Orthorhombic  Forms, 

57 

Compound  Tetragonal  Forms,  691 
Contact    Twins,    151-153,    247- 

253,  257 
Cooke,  J.  P.,  xiii 
Corundum,   74,   76,    80,   81,   83, 

104,  235 
Crystal,  2,  3 

Crystal,  Compound,  25,  26 
Crystal  Models,  viii,  56 
Crystal,  Number  of  Forms  on, 

39 
Crystal,  Simple,  25 


Crystalline  Aggregate,  149,  247 
Crystalline  Minerals,  148 
Crystallographic  Axes,  how  rep- 
resented, 161 
Crystallographic  Drawings, 

Beading  of,  28-34,  46,  47 
Crystallographic         Nicknames, 

188-202 
Crystallograpmc    Nomenclature, 

187-202 
CrystaAlographic  Shorthand,  28- 

34,  46,  47,  57,  70,  75,  109-113 
Crystallographic  Symmetry,  161- 

166 

Crystallography,  2 
Crystallography,  Books  relating 

to  that  subject,  x-xiii 
Crystallography,   location   of    a 

point,  3-6 
Crystallography,    Mathematical, 

5 
Crystallography,     Methods     of 

Study,  v-x,  xiv-xvi 
Cube,   123,   126,  141,   142,   183- 

186,  188,  200,  204,  208,  236- 

248,  253,  254 
Cubical  Cleavage,  155,  159 
Cubic  Axes,  131,  139 
Cuproid,  201 
Cyclic  Twin,  153,  252,  253 

Dana,  E.  S.,  34,  46,  74,  167 
Dana,  E.  S.,  Text  Book  of  Min- 
eralogy, x,  167 
Dana,  J.  D.,  xiii,  28,  32,  33,  34, 

46,  70,  74,  112 

Dana,    Notation,    29,    32,    46, 

47,  70,  112 

Dana's   Division  of   the   Hexa- 
gonal   System,    74 
Deltohedron,  200 


INDEX. 


269 


Deltoid  Dodecahedron,  124,  132, 
133,  142,  143,  183,  185,  200 

Deltoid  Icosi  Tetrahedron,  201 

Des  Cloizeaux,  A.,  29 

Diagonal  Prism,  192 

Diametral  Prism,  191 

Diametral  Pyramid,  195 

Diamond,  3,  149,  loO,  153,  204 

Dido  decahedron,  125,  137,  138, 
144,  185,  197,  201 

Dihexagonal  Bipyramidal  Class, 
182,  183 

Dihexagonal  Henri  Di  Dode- 
cahedron, 198 

Dihexagonal  Prism,  81-85,  99, 
101,  105,  179,  181-183,  192 

Dihexagonal  Pyramid,  82,  93, 
95,  101,  107,  182,  183,  197, 
206 

Dihexagonal  Pyramidal  Class, 
182 

Dihexagonal  Scalenohedron,  197 

Dihexagonal  Trapezohedron,  198 

Dihexahedron  of  the  Principal 
Series,  196,  197 

Dihexahedron  of  the  Second 
Order,  197 

Dioctahedral  Prism,  191 

Dioctahedron,  62,  195 

Diplagihedron,  198 

Diplohedron,  202 

Diploid,  125,  137,  138,  144, 
185,  202 

Diploid,  Symmetry  of,  51,  52, 
138 

Diplo-Pyritohedron,  202 

Diplo-Pyritoid,  202 

Diplo-Tetrahedron,  195 

Directions  for  Studying  Hexa- 
gonal Crystals,  121 

Directions  for  Studying  Iso- 
metric Crystals,  147 


Directions  for  Studying  Mono- 
clinic  Crystals,  49 

Directions  for  Studying  Ortho- 
rhombic  Crystals,  59 

Directions  for  Studying  Tetra- 
gonal Crystals,  72 

Directions  for  Studying  Tre- 
clinic  Crystals,  38,  39 

Direct  Octahedron,  194 

Direct  Prism,  191 

Direct*  Pyramid,  194 

Direct  Tetragonal  Prism,  61, 
63,  175,  176,  191 

Direct  Tetragonal  Pyramid,  61, 
63,  175,  176,  194 

Disphene,  195 

Distinction  between  Mineral 
Cleavage  and  Eock  or  Slaty 
Cleavage,  160 

Distinction  between  Parting 
Structure  and  Cleavage  Struc- 
ture, 159,  160 

Distinction  between  the  Positive 
and  Negative  Dyakis  Dode- 
cahedrons, 137 

Distinction  between  the  Positive 
and  Negative  Hexakis  Tetra- 
hedrons, 135 

Distinction  between  Holohedral 
and  Hemihedral  iorms,  46 

Distinction  between  Orthorhom- 
bic  and  Tetragonal  Sphenoids, 
65,  66 

Distinction  between  the  Positive 
and  Negative  Pentagonal  Do- 
decahedrons, 136,  137 

Distinction  between  the  Positive 
and  Negative  Tetragonal 
Triakis  Tetrahedrons,  133 

Distinction  between  the  Positive 
and  Negative  Tetrahedrons, 
132 


270 


INDEX. 


Distinction  between  the  Positive 
and  Negative  Tetrahedral 
Pentagonal  Dodecahedrons, 
140,  141 

Distinction  between  the  Positive 
and  Negative  Trigonal  Triakis 
Tetrahedrons,  134 

Distinction  between  Primary 
and  Secondary  Tetragonal 
Prisms,  64 

Distinction  between  Primary 
and  Secondary  Tetragonal 
Pyramids,  65 

Distinction  between  the  Bight- 
handed  and  Left-handed  Pen- 
tagonal Icositetrahedrons, 
138,  139 

Distinction  between  Tetragonal 
Sphenoids  and  Scalenohe- 
drons,  66 

Distinction  "between  the  Tetra- 
gonal and  Hexagonal  Sys- 
tems, 73,  74 

Distinguishing  Characteristics 
of  Hexagonal  Crystals,  76 

Distinguishing  Characteristics 
of  the  Isometric  Crystals,  123 

Distinguishing  Characteristics 
of  Monoclinic  Crystals,  44 

Distinguishing  Characteristics 
of  Orthorhombic  Crystals, 
53,  54 

Distinguishing  Characteristics' 
of  Tetragonal  Crystals,  62 

Distinguishing  Characteristic^ 
of  Triclinic  Crystals,  19-21 

JDitetragonal-Bipyramidal  Class, 
175,  176 

Ditetragonal    Octahedron,    195 

Ditetragonal  Prism,  61,  63,  98, 
99,  174,  191 


Ditetragonal   Pyramid,    62,    63, 

121,  175,  176,  195 
Ditetragonal    Pyramid    of    the 

First  Direction,  195 
Ditetragonal    Pyramidal    Class, 

175 
Ditetragonal    Pyramidal    Class, 

Symmetry  of,  175 
Ditetragonal  Scalenohedron,  195 
Ditrigonal    Bipyramidal    Class, 

179,  180 
Ditrigonal  Prism,   98,  99,   105, 

177,  179,  180,  192 
Ditrigonal   Prism  of  the   First 

Order,  192 
Ditrigonal       Prism       of       the 

Second  Order,  193 
Ditrigonal     Pyramid,     95,     96, 

107,  179,  180,  198 
Ditrigonal      Pyramidal      Class, 

178,  179 

Ditrigonal  Pyramid,  Symmetry 

of,  96 
Ditrigonal    Pyramidal    Tetarto- 

hedral  Class,  178 
Ditrigonal  Scalenohedral  Class, 

179 

Ditrigonal    Trapezohedron,    199 
Dodecagonal  Prism,  192 
Dodecahedral  Axes,  131,  139 
Dodecahedral  Class,  183,  184 
Dodecahedral  Cleavage,  155, 159 
Dodecahedron,    123,    126,    127, 

141-144,    183-186,    200,    204, 

207,  236,  239-244,  248,  254 
Dodecahedron,  Dyakis,  51,  125, 

135,  137,  138,  144,  185,  188, 

201,  202,  215,  238,  245,  246, 

254,  261 
Dodecahedron,  Pentagonal,  24, 

25,  51,  52,  125,  135-138,  142, 


INDEX. 


271 


143,  183,   185,  200,  207,  237, 

238,  244-246,  254 
Dodecahedron,     Rhombic,     123, 

126,    127,    141-143,    183-186, 

200,  204,   207,   236,    239-244, 
248,  254 

Dodecahedron,  Tetrahedral  Pen- 
tagonal, Symmetry  of,  123, 
141,  166,  261 

Dodecahedron,  Tetrahedral  Pen- 
tagonal, 123,  125,  140-142, 

144,  166,  183,  184,  202,  238, 

239,  261 

Domatic  Dodecahedron,  200 

Domatic  Class,  169,  170 

Dome,  12,  13,  21,  42-45,  50,  54 

Dome,  Primary,  170 

Dome,  Quaternary,  170 

Dome,  Tertiary,  170 

Dome,  Vertical,  43,  44 

Dominant  Form,  26 

Drawings,  Crystallographic,  28- 

34 
Dyakis  Dodecahedron,  51,  125, 

135,  137,  138,  144,  185,  188, 

201,  202,  215,  238,  245,  246, 
254,  261 

Dyakis  Dodecahedral  Class,  184, 
185 

Dyakis-Dodecahedron,  Symme- 
try of,  51,  52,  138,  261 

Edges,  Ehombohedral,  86,  106 
Edges,  Zigzag,  of  the  Rhombo- 

hedron     and     Scalenohedron, 

86,  89,  90 

Eight  Angled  Dodecahedron,  197 
Eight  Angled  Hexahedron,  196 
End  Plane,  199 
Epsomite,  55,  61,  216 


Family  Names,  Change  in,  188, 

189 
Family    of    Hexagonal   Prisms, 

191-193 
Family  of  Hexagonal  Pyramids, 

196-199 
Family    of    Monoclinic   Prisms, 

190 
Family  of  Monoclinic  Pyramids, 

193 
Family  of  Orthorhombic  Prisms, 

190,  191 

Family  of  Orthorhombic  Pyra- 
mids, 194 
Family   of   Tetragonal   Prisms, 

191 
Family  of  Tetragonal  Pyramids, 

194-196 
Family     of     Triclinic     Prisms, 

189,  190 
Family  of   Triclinic  Pyramids, 

193 
Families  of  the  Isometric  Tribe, 

200-202 
Families  ol  the  Pinacoid  Tribe, 

199,  200 
Families   of   the   Prism    Tribe, 

189-193 
Families  of  the  Pyramid  Tribe, 

193-199 

First  Hexagonal  Prism,  191 
First      Hemimorphic     Tetarto- 

hedral  Class,  180,  181 
First  Horizontal  Prism,  190, 191 
First      Order      of      Hexagonal 

Prism,    80-85,    91,    101,    104, 

177,  179-183,  191 
First  Order  of  Hexagonal  Pyra- 
mid, 81-85,  93,  102,  106,  181- 
183,   188,   196 


272 


INDEX. 


First  Order  Bhombohedron,  88, 
97,  106,  177,  179,  196 

First  Order,  Tetragonal  Prism, 
61,  63,  175,  176,  191 

First  Order,  Tetragonal  Pyra- 
mid, 61,  63,  175,  176,  194 

Fivelings,  152,  256,  257 

Fluoroid,  200 

Fluorite,  27,  123,  141,  149,  150, 
153,  208 

Foote  Mineral  Company,  viii 

Form,  22-25 

Forms  of  the  Hexagonal  Sys- 
tem, 76-80 

Fourlings,  152 

Frankenheim,  M.  L.,  167 

Frederick  Barbarossa,   188 

Fundamental  Bhombohedron,  87 

Gadolin,  A.,  161,  167 

Galenoid,  200 

Galenite,  3,  14,  23,  26,  27,  123, 
141,  149,  150,  153,  204,  207, 
253,  254 

Garnet,  27,  123,  141,  207 

Garnet  Crystallization,  200 

Garnet  Dodecahedron,  200 

Garnetohedron,  200 

Garnetoid,  200 

Geniculated  Twin,  153,  252 

Goslarite,  51,  57,  214,  216' 

Groth,  P.,  29,  34,  167,  173 

Groth,  Divisions  of  the  Hexa- 
gonal System,  74 

Groth  'a  Notation,  29 

Group,  Hexagonal,  Trapezo- 
hedron,  93-95,  164 

Groups,  Parallel,  3,  149,  150, 
204,  205,  247 

Group,  Pyramidal  Hexagonal, 
91-93,  121,  164 


Group,  Pyramidal  Tetragonal, 
67-69,  163,  174,  175 

Group,  Ehombohedral,  85-91, 
121,  164 

Group,  Sphenoidal  Tetragonal, 
65-67,  163,  173,  174 

Group,  Tetartohedral  Ehombo- 
hedron,  96-98,  164 

Group,  Trapezohedral  Hexa- 
gonal, 94,  164 

Group,  Trapezohedral  Tetarto- 
hedral, 98-100,  164 

Group,  Trapezohedral  Tetra- 
gonal, 69,  163 

Group,  Trigonal  Hexagonal, 
95,  96,  164 

Group,  Trigonal  Tetartohedral, 
101,  102,  164,  165 

Growths,  Parallel,  3,  149,  150, 
204,  205,  247 

Growths,  Polysynthetic,  151, 
153,  247 

Gypsum,  3,  11,  12,  15,  17,  18, 
26,  41,  43-47,  149,  150,  152, 
203,  210,  248,  249 

Gyroid,  123,  125,  139,  142,  144, 
166,  184,  188,  202,  238,  261 

Gyroidal  Group,  184 

Gyroidal  Hemihedral  Forms, 
123,  125,  138,  139,  142,  144, 
166,  184,  202,  238,  261 

Gyroidal  Hemihedral  Forms, 
Symmetry  of,  139,  166,  261 

Gyroid  Hemihedral  Class,  184 

Gyroids  in  Combination  with 
•  other  forms,  142 

Harmotome,  149,  150,  153,  256 
Harvard  University,  v 
Hauy-L6vy-Des    Cloizeaux    No- 
tation,  29 


INDEX. 


273 


Haiiynite,  149,  150,  153,  253 
Hematite,  149,  150,  153,  255 
Henri  Brachy  Dome,  190 
Hemi  Di  Hexagonal  Prism,  192 
Henri   Di   Hexagonal   Pyramid, 

197,   198 

Hemi  Di  Octahedron,  195 
Hemi-Ditetragonal    Prism,     67, 

191 
Hemi-Ditetragonal  Pyramid,  67, 

68,  195,  196 

Hemi  Dodecahedron,  197 
Hemi     Dodecahedron     of     the 

First    Order,    196 
Henri-Dome,  25,  45,  55,  190 
Hemihedral      and      Bolohedral 

Forms,    Distinction    between, 

46 
Hemihedral    Class,    Monoelinie, 

45,  162,  169,  170,  208-211,  258 
Hemihedral  Di  Hexahedron,  198 
Hemihedral  Forms,  24,  25,  45, 

46,  55-57,  65-69,   85-96,  131- 
139 

Hemihedral  Forms   Denned,  25 

Hemihedral  Forms,  Symmetry 
of,  24 

Hemihedral  Gyroidal  Forms, 
123,  125,  138,  139,  142,  144, 
166,  184,  202,  238,  261 

Hemihedral  Hexagonal  Forms, 
77,  85-96,  121,  164,  176-182, 
207,  215,  223,  229-235 

Hemihedral  Isometric  Forms, 
123-125,  131-139,  141-144, 
165,  166,  200,  201,  207,  215, 
236-238,  242-246,  253,  254, 
261 

Hemihedral  Monoelinie  Forms, 
45,  46,  161,  162,  169,  170,  258 

Hemihedral  Notation,  36-38 


Hemihedral  Oblique  Forms,  124, 

131-135,    141-144,    165,    185, 

186,   236,   237,   242-244,   253, 

254 
Hemihedral  Orthorhombic  Form, 

55,  56, 162,  163, 170,  171,  259 
Hemihedral      Parallel      Forms, 

125,    135-138,    141-144,    166, 

200-202,    207,    215,   237,   238, 

244-246,    254 
Hemihedral  Plagihedral  Forms, 

123,  125,  138,  139,  142,  144, 

166,  184,  202,  238,  261 
Hemihedral    Pyramidal    Group, 

Symmetry  of,  93,  164,  260 
Hemihedral  Rhombohedral 

Group,  Symmetry  of  52,  90, 

91,   164,   259 
Hemihedral  Tetragonal  Forms, 

65-69,  163,  220,  221,  259 
Hemihedral  Trapezohedral 

Group,  Symmetry  of,  94,  164, 

260 
Hemihedral     Trigonal     Group, 

Symmetry  of,  96,  164,  260 
Hemi  Hexagonal  Scalenohedron, 

198,  199 

Hemi  Hexakis  Octahedron,  201 
Hemi  Icosi  Tetrahedron,  201 
Hemi  Macro  Dome,  190 
Hemimorphic  Class,  178,  179 
Hemimorphie  Class,  Monoelinie, 

169 
Hemimorphic  Forms,  45,  46,  56, 

57,  102-104 

Hemimorphic  Group,  182 
Hemimorphic     Group     of     the 

Pyramidal  Hemihedral  Class, 

Tetragonal,  172,  173,  261 
Hemimorphic      Group,      Tetra- 
gonal, 175 


274 


INDEX. 


Hemimorphic  Hemihedral  Class, 

178-182 
Hemimorphie  Hemihedral  Class, 

Tetragonal,  175 
Hemimorphic  Hemihedral  Class, 

Tetragonal,  172,  173,  261 
Hemimorphic  Hexagonal  Forms, 

80,  102-104,  108,  109,  165 
Hemimorphic  Hexagonal  Form, 

Symmetry  of,  103,  104,  165, 

260 
Hemimorphic  Holohedral  Class, 

182 
Hemimorphic  Holohedral  Class, 

Tetragonal,  175 
Hemimorphic          Orthorhombic 

Forms,  56,  57,  163,  171,  259 
Hemimorphic          Orthorhombic 

Forms,  Symmetry  of,  56,  163, 

259 

Hemimorphic  Pyramidal  Hemi- 
hedral Class,  180,  181 
Hemimorphic         Rhombohedral 

Hemihedral  Class,  178,  179 
Hemimorphic          Tetartohedral 

Class,  176,  177 
Hemimorphie          Tetartohedral 

Class,    Tetragonal,   172,    173, 

261 

Hemimorphic    Trigonal    Hemi- 
hedral Class,  178,  179 
Hemimorphie  Trigonal  Tetarto- 
hedral Class,  176,  177 
Hemimorphism,  45,  46,  56 
Hemi  Octahedron,  45,  200 
Hemi  Octakis  Hexahedron,  201 
Hemi-Ortho-Dome,  45,  190 
Hemiorthotype,  193 
Hemipinacoidal  Class,  167,  261 
Hemi  Primary  Hexagonal  Prism, 

192 


Hemi  Primary  Hexagonal  Py- 
ramid, 196 

Hemi-Prism,  25,  55,  189 

Hemi-Pyramid,  3, 11,  12,  15,17, 
18,  26,  41,  44-46,  47,  55,  203 

Hemi  Secondary  Hexagonal 
Prism,  192 

Hemi  Secondary  Hexagonal 
Pyramid,  197 

Hemi  Tetragonal  Triakis  Octa- 
hedron, 201 

Hemi  Tetragonal  Pyramid,  194 

Hemi  Tetrakis  Hexahedron,  200 

Hemi  Trigonal  Triakis  Octa- 
hedron, 201 

Hessel,  J.  F.  C.,  167 

Hexagonal  and  Orthorhombic 
Crystals,  Distinction  between, 
52 

Hexagonal  and  Tetragonal  Sys- 
tems, Distinctions  between, 
73,  74 

Hexagonal  Axes,  8,  73,  75,  109, 
203 

Hexagonal  Basal  Pinacoid,  176- 
183 

Hexagonal  Bipyramidal  Class, 
181,  182 

Hexagonal  Cleavage,  158 

Hexagonal  Compound  Forms, 
104 

Hexagonal  Crystals,  Directions 
for  Studying,  121 

Hexagonal  Crystals,  distinguish-, 
ing  Characteristics  of,  76 

Hexagonal  Crystals,  Beading 
Drawings  of,  109-113 

Hexagonal  Division,  74,  121 

Hexagonal  Dodecahedron  of 
the  First  Order,  196 


INDEX. 


275 


Hexagonal  Dodecahedron  of  the 

Second  Order,  197 
Hexagonal    Hemihedral,     Sym- 
metry of,  90,  91,  93,  94,  96, 

164,  259,  260 
Hexagonal  Hemimorphic  Class, 

182 
Hexagonal  Hemimorphic  Forms, 

102-104,  108,  109 
Hexagonal  Hemimorphic  Forms, 

Symmetry  of,  103-104, 165,  260 
Hexagonal  Holohedral  Symme- 
try, 74,  84,  85,  163,  259 
Hexagonal  Lateral  Axes,  73 
Hexagonal  Nomenclature,  75 
Hexagonal  Parallel  Growths,  3, 

28,  149,  205 

Hexagonal  Pinacoid,  76, 176, 183 
Hexagonal    Planes,    Rules    for 

naming  them,  104-109 
Hexagonal  Primary  Prism,   61, 

63,  80-85,  91,  101,  104,  177, 

179-183,   191 
Hexagonal    Primary    Pyramid, 

81-85,  93,  102,  106,  181-183, 

188,  196 

Hexagonal  Prism,  189,  204 
Hexagonal  Prism  of  the  First 

Order,    80-85,    91,    101,    104, 

177,  179-183,  191 
Hexagonal  Prism  of  the  Prin- 
cipal Series,  191 
Hexagonal  Prism  of  the  Second 

Order,  81-85,  91,  93,  99,  101, 

105,  177,  179-183,  192 
Hexagonal  Prism  of  the  Second 

Series,  192 
Hexagonal  Prism  of  the  Third 

Order,  91,  92,  105,  181,  18:2, 

192 
Hexagonal      Pyramidal     Class, 

18,  181 


Hexagonal  Pyramidal  Group, 
91-93,  121,  164 

Hexagonal  Pyramidal  Tetarto- 
hedral  Class,  180,  181 

Hexagonal  Pyramid  of  the  First 
Division,  196 

Hexagonal  Pyramid  of  the  First 
Order,  81-85,  93,  102,  106, 
181-183,  188,  196,  204 

Hexagonal  Pyramid  of  the 
Second  Division,  197 

Hexagonal  Pyramid  of  the 
Second  Order,  82-85,  96,  106, 
179-183,  196,  197 

Hexagonal  Pyramid  of  the  Third 
Order,  91-93,  181,  182,  198 

Hexagonal  Pyramidohedron  of 
the  First  Normal  Direction, 
196 

Hexagonal  Pyramidohedron  of 
the  Second  Normal  Direction, 
197 

Hexagonal  Scalenohedron,  88- 
91,  94,  97,  100,  107,  179,  197, 
207,  215,  223-227,  231,  234 

Hexagonal  Scalenohedron,  La- 
teral Edges,  89,  107 

Hexagonal  Secondary  Prism,  81- 
85,  91,  93,  99,  101,  105,  177, 
179-183,  192 

Hexagonal  Secondary  Pyramid, 
82-85,  96,  106,  179-183,  196, 
197 

Hexagonal  Semi-Axes,  Nota- 
tion for,  75 

Hexagonal  Shorthand  or  Nota- 
tion, 114-120 

Hexagonal  System,  8,  52,  73-121, 
203-207,  215,  221-235,  249- 
255,  254,  255,  259,  260 

Hexagonal  System,  Divisions 
of,  74 


276 


INDEX. 


Hexagonal    System,    Symmetry, 

of,  25,  74,  76,  84,  85,  90,  91, 

93,  94,  96,  100,  102,  163-165, 

259,  260 
Hexagonal  Tertiary  Prism,  91, 

92,  105,  181,  182,  192 
Hexagonal  Tetartohedral  Forms, 

96-102 
Hexagonal  Tetartohedral  Form, 

Symmetry  of,   100,  102,  164, 

165,  260 
Hexagonal  Trapezohedral  Class, 

181 
Hexagonal     Trapezohedral 

Group,  93-95,  164 
Hexagonal    Trapezohedron,    93- 

95,  107,  121,  181,  198 
Hexagonal      Trigonal      Group, 

95,  96,  164 

Hexahedral    Pentagonal    Dode- 
cahedron, 200 

Hexahedral  Trigonal  Icosi  Te- 
trahedron, 200 
Hexahedron,  Tetrakis,  123,  127, 

128,  135,   136,   141-143,  184- 

186,   189,   200,   208,   236-238, 

240,  244,  248 
Hexahedron,  123,  126,  141,  142, 

183-186,   188,   200,    208,   236- 

248,   253,  254 
Hexoctahedron,    124,    130,    137, 

144,  186,  188,  201,  207,  236- 

239,  241,  242 
Hexakis   Octahedron,    124,   130, 

137,  144,  186,  188,  201,  207, 

236-239,  241,  242 
Hexakis  Tetrahedral  Class,  185, 

186 
Hexakis  Tetrahedron,  124,  134, 

135,  144,  186,  201,  237,  244, 

261 


Hextetrahedral  Class,  185,  186 
Hextetrahedron,   124,   134,   135, 

140,  144,  186,  201,  237,  244, 

261 
Holohedral      and      Hemihedral 

Forms,    Distinction    between, 

46 

Holohedral  Class,  182,  183 
Holohedral    Forms,    Symmetry, 

of,  23,  24 
Holohedral     Hexagonal     Class, 

182,  183 
Holohedral     Isometric     Forms, 

123-131,    141-144,    165,    186, 

200,   201,   236,   239-242,   247, 

248,  253,  254,  261 
Holohedral      Isometric      Forms 

Symmetry  of,   123,  130,   131, 

165,  261 
Holohedral  Isometric  Forms  in 

Combination,  141 
Holohedral    Class,    Monoclinic, 

45,  162,  170,  208-211,  258 
Holohedral    Class,    Ortborhom- 

bie,  171,  172,  259 
Holohedral    Class,    Tetragonal, 

175,  176 
Holohedral  Class,  Triclinic,  23, 

162,  168,  169,  205,  206,  258 
Holohedral  Forms,  23,   24,  45, 

46,  54-57,   63-65,  80-8^,   125- 
131 

Holohedral  Group,  182,  183 

Holohedral  Hexagonal  Form, 
76,  80-85,  121,  163,  204,  206, 
221-224,  226-228,  233-235 

Holohedral  Hexagonal  Symme- 
try, 84,  85,  163,  259 

Holohedral  Monoclinic  Forms, 
45,  162,  170,  208-211,  258 

Holohedral  Orthorhombio  Forms, 
54,  55,  162,  171,  172,  259 


INDEX. 


277 


Holohedral    Tetragonal   Forms, 

63-65,   163,  216-220,  259 
Horizontal  Prism,  190-191 
Horizontal   Prism   of   a  Rhom- 
bohedral  Section,  190 

Icositetrahedron,  124,  129,  141- 

144,   201,   236,  237,   240-242, 

244-246 
Icositetrahedrons,     Pentagonal, 

123,  125,  138,  139,  142,  144, 

166,  184,  202,  238,  261 
Inclined  Axis,  42 
Inclined-Faced  Hemihedral 

Class,  185,  186 
Inclined       Hemihedral      Class, 

185,  186 

Individual  Names,  187,  188 
Indices,  32-34,  75 
Inorganic  World,  1 
Inscribed  Rhombohedron,   90 
Inverse  Octahedron,  195 
Inverse  Prism,  191 
Inverse  Pyramid,  195 
Inverse   Tetragonal   Prism,   61, 

63,  175,  176,  191 
Inverse  Tetragonal  Pyramid,195 
lodyrite,    /4,    76,    80,    81,    102, 

104,  222 
lodyrite  Type,  74,  76,  81,  102- 

104,  108,  121,  165,  222 
lodyrite    Type,    Symmetry    of, 

103,  165,  260 

Irregular  Tetrahedron,  194 
Isometric     and      Orthorhombic 

Crystals,  Distinction  between, 

51,  52 

Isometric  Axes,  7,  122,  126,  203 
Isometric  Cleavage,  159 
Isometric      Compound     Forms, 

141,  142 


Isometric  Crystals,  Directions 
for  Studying,  147 

Isometric  Crystals,  Distinguish- 
ing Characteristics  of,  123 

Isometric  Gyroidal  Hemihedral 
Forms,  Symmetry  of,  139, 
166,  261 

Isometric,  Hemihedral  Forms, 
123-12o,  131-139,  141-144, 
165,  166,  200,  201,  207,  215, 
236-238,  242-246,  253,  254, 
261 

Isometric  Hemihedral  Forms, 
Symmetry  of,  51,  52,  123, 
135,  138,  139,  165,  261 

Isometric  Holohedral  Forms, 
123-131,  141-144,  165,  186, 
200,  201,  236,  239-242,  247, 
248,  253,  254,  261 

Isometric  Holohedral  Forms, 
Symmetry  of,  23,  24,  123, 
130,  131,  165 

Isometric  Hemihedral  Oblique 
Forms,  Symmetry  of,  123, 
135,  165,  261 

Isometric  Parallel  Hemihedral 
Forms,  51,  52,  123,  138,  166, 
261 

Isometric  Shorthand  or  Nota- 
tion, 146,  147 

Isometric    System,    7,    122-147, 

165,  166,   183-186,   189,   200- 
204,   207,   208,   215,   236-248, 
253,  254,  261 

Isometric  System,  Symmetry  of, 
23,  24,  51,  52,  123,  130,  131, 
135,  138,  139,  141,  147,  165 

166,  261 

Isometric  Tetartohedral  Forms, 
123,  125,  140-142,  144,  166, 
183,  184,  202,  238,  239,  261 


278 


INDEX. 


Isometric  Tetartohedral  Forms, 
Symmetry  of,  123,  141,  166, 
261 

Isometric  Tribe,  189,  200-202 
Isometric  Twins,  247,  248,  253, 
254 

Jointing,  Bock,  160 
Johnson,  Ben,  188 

Klinorhombohedral  Prism,  189 
Krantz,  F.,  viii 
Kraus,  E.  H.,  167 
Kuntze,  Otto,  viii 

Lateral  Angles,   Bhombohedral, 

86,  87 

Lateral  Axes,  10,  42,  60,  73 
Lateral  Axes  Hexagonal,  73 
Lateral  Axes,  Monoclinic,  42 
Lateral  Axes,  Tetragonal,  60 
Lateral  Axes,  Triclinic,  10 
Lateral  Edges,  Hexagonal  Scale- 

nohedron,  89,  107 
Lateral    Edges,    Bhombohedral, 

86,  106 
Left-handed   Ditrigonal   Prism, 

98,  99,  193 

Left-handed    Hexagonal    Pyra- 
mid of  the  Third  Order,  91- 
93,  198 
Left-handed  Hexagonal   Trape- 

zohedron,  93-95,  198 
Leit-handed    Negative    Bhomb- 
ohedron,  96-98,  198 
Left-handed     Negative     Tri- 
gonal Pyramid,  98-100 
Left-handed    Pentagonal   Icosi- 
tetrahedron,  125,  138,  139, 184 
Left-handed  Positive  Secondary 
Bhombohedron,  96,  97 


Left-handed  Positive  Tertiary 
Bhombohedron,  96-98,  198 

Left-handed  Positive  Trigonal 
Pyramid,  98-100 

Left-handed  Secondary  Tri- 
gonal Prism,  98,  99,  176,  192 

Left-handed  Sphenoid,  56 

Left-handed  Tetrahedral  Penta- 
gonal Dodecahedron,  125, 
140,  141,  184 

Left-handed  Tertiary  hexagonal 
Prism,  91-93,  192 

Left-handed  Tertiary  Hexagonal 
Pyramid,  91-93,  198 

Left-handed  Tertiary  Trigonal 
Prism,  101,  102,  193 

Left-handed  Tertiary  Trigonal 
Pyramid,  101,  102,  199 

Left-handed  Tetragonal  Trape- 
zohedron,  69,  196 

Leucite  Crystallization,  201 

Leucitohedron,  124,  129,  141- 
144,  201,  236,  237,  240-242, 
244-246 

Leucitoid,  129,  141-144,  201 

Levy,  A.,  29 

Liebisch,  T.,  34,  74 

Limonite,  148 

Lines,  broken,  161 

Lines,  full,  161 

Linnseite,  3,  19,  23,  26,  123,  141, 
204 

Literature  of  Crystallography, 
x-xiii 

Lithium  Sulphate,  169 

Longfellow,  Henry  Wadsworth, 
188 

Macro-Axis,  10 
Macro-Diagonal,  10 
Macro-Diagonal  Pinacoid,   200 


INDEX. 


279 


Macro-Diagonal  Prism,   191 

Macro-Dome,  12,  22,  54, 190, 191 

Macro-Pinacoidal  Cleavage, 

155-157 

Macro-Pinacoid,  12,  21,  54,  200, 
205 

Macro-Semi-Axis,  50 

Magnetite,  3,  14,  23,  123,  128, 
204 

Mallard,  E.,  34 

Marcasite,   149,   150,   154,   256, 
257 

Melanterite,  41-47,  208,  210 

Mellite,  61,  70,  73,  74,  218 

Method   01    Representing   Sym- 
metry, 161,  162 

Michigan  College  of  Mines,  vi 

Miller,  W.  H.,  xiii,  32,  33,  34, 
37,  47,  70,  7* 

Miller,  Axes  of  Hexagonal  Sys- 
tem, 74 

Miller-Bravais     Notation,      29, 
75,  103,  111 

Miller  Notation,  32-34,  47,  70 

Milton,  John,  188 

Mimicry,  153,  154,  256-258 

Mineral,  2,  3 

Mineral  Aggregate,  149, 160,  247 

Mineral  Chemistry,  2 

Mineral  Kingdom,  1 

Mineralogy,  1,  2 

Mineralogy,       Instruction       in, 
viii,  xv 

Models,  Crystal,  vii,  56 

Monoclinic  Axes,   7,   40-42,  47, 

203 

Monoclinic  Cleavage,  157 
Monoclinic  Clino-Dome,  43,  44, 

190,  203 

Monoclinic    Clinohedral   Forms, 
46,  161,  162,  169,  170,  258 


Monoclinic  Clino  Pinacoids,  43 
Monoclinie  Clino  Prism,  190 
Monoclinic  Compound  Forms,  46 
Monoclinic  Crystals,   Directions 

for  Studying,  49 
Monoclinic      Crystals,      Distin- 
guishing Characteristics  of,  44 
Monoclinic     Crystals,     Beading 

Drawings  of,  46,  47 
Monoclinic   Crystals,   Symmetry 
of,  40,  41,  44,  49,  162,  169, 
258,    261 
Monoclinic  Domes,  43,  44,  170, 

190 

Monoelinic  Forms,  48 
Monoclinic   Hemihedral   Forms, 
45,    46,    161,    162,    169,    170, 
2oS 

Monoclinic   Hemihedral   Forms, 

Symmetry  of,  40,  41,  162,  258 

Monoclinic  Hemimorphic  Forms, 

45,  46,  163,  169 
Monoclinic  Hemimorphic  Forms, 

Symmetry  of,  169,   261 
Monoclinic   Hemimorphism,    45, 

46 
Monoclinic   Hemi  Ortho   Dome, 

190 
Monoclinic  Hemi  Pyramid,  193, 

203 
Monoclinic    Holohedral    Forms, 

45,  162,  170,  208-211,  258 
Monoclinic    Holohedral    Forms, 
Symmetry  of,  40,  41,  162,  258 
Monoclinic  Nomenclature,  41-43 
Monoclinic  Notation,  46-48 
Monoclinic     Ortho-Domes,     43, 

44,  190 

Monoclinic  Ortho  Pinacoids,  43, 
44 


280 


INDEX. 


Monoclinic  Pinacoids,  42-44, 
169,  170 

Monoclinic  Planes,  relation  to 
the  Axes,  43 

Monoclinic  Planes,  Rules  for 
naming,  44,  45 

Monoclinic  Prisms,  43,  44,  170, 
190,  203 

Monoclinic  Pyramid,  43,  45, 
193,  203 

Monoclinie  Shorthand  or  Nota- 
tion, 48 

Monoclinic  Symmetry,  40,  41, 
44,  49,  162,  169,  258,  261 

Monoclinic  System,  7,  40-49, 
162,  169,  170,  203,  208-211, 
248,  250,  255,258,  261 

Monoclinic  Vertical  Dome,  190 

Monoclinic  Vertical  Prism,  190 

Moses,  A.  J.,  x,  74,  167,  173 

Moses  and  Parsons.  Elements 
of  Mineralogy,  x,  167,  173 

Moses,  Division  of  the  Hexa- 
gonal System,  74 

Names  of  Individuals,  187,  188 
Natron,  8,  11,  12,  17,  18,  26,  41, 

44,  46,  47,  203 
Naumann,  C.  F.,  xiii,  29,  32,  33, 

47 
Naumann  Notation,  29,  32,  33, 

47,  70,  111,  112 
Negative  Ditrigonal  Prism,  98, 

99,  192 
Negative    Ditrigonal    Pyramid, 

95,  96,  199 
Negative  Dyakis  Dodecahedron, 

51,  125,  135,  137,  138,  215 
Negative  Forms,  36 
Negative    Hexagonal    Pyramid 

of  the  Third  Order,  91-93,  198 


Negative  Hexagonal  Scaleno- 
hedron,  89,  197 

Negative  Hexagonal  Semi-Axes, 
109,  110 

Negative  Hexagonal  Trapezo- 
hedron,  93,  94 

Negative  Hexakis  Tetrahedron, 
124,  135,  186 

Negative  Left-Handed  Tertiary 
Trigonal  Prism,  193 

Negative  Left-handed  Tertiary 
Trigonal  Pyramid,  199 

Negative  Left-Hanaed  Tertiary 
Ehombonedron,  198 

Negative  Left-handed  Trigonal 
Trapezohedron,  199 

Negative  or  Left-Handed  Ter- 
tiary Hexagonal  Pyramid, 
198 

Negative  or  Left-Handed  Hexa- 
gonal Prism,  192 

Negative  or  Left-Handed  Or- 
thorhombic  Sphenoid,  194 

Negative  or  Left-handed  Tetra- 
gonal Trapezohedron,  196 

Negative  or  Left-Handed  Tri- 
gonal Prism,  192 

Negative  or  Left-Handed  Tri- 
gonal Pyramid,  197 

Negative  Pentagonal  Dodeca- 
hedron, 125,  136,  137, 185,  20T 

Negative  Primary  Trigonal 
Prism,  101,  176,  192 

Negative  Primary  Trigonal 
Pyramid,  101,  102 

Negative  Ehombohedron,  85-88, 
198 

Negative  Ehombohedron  of  th« 
Second  Order,  197 

Negative  Eight-Handed  Ter- 
tiary Ehombohedron,  198 


INDEX. 


281 


Negative  Eight-Handed  Ter- 
tiary Trigonal  Prism,  193 

Negative  Eight  -handed  Tertiary 
Trigonal  Pyramid,  199 

Negative  Right-handed  Trigonal 
Trapezohedron,  199 

Negative  Scalenohedron,  197 

Negative  Secondary  Rhombo- 
hedron,  96,  97,  197 

Negative  Secondary  Trigonal 
Prism,  98,  99,  176,  192 

Negative  Secondary  Trigonal 
Pyramid,  98-100,  197 

Negative  Sphenoid,  56,  195 

Negative  Tertiary  Trigonal 
Prism,  101,  102,  193 

Negative  Tertiary  Trigonal 
Pyramid,  101,  102,  199 

Negative  Tertiary  Hexagonal 
Prism,  91,  93,  192 

Negative  Tertiary  Hexagonal 
Pyramid,  91-93,  198 

Negative  Tertiary  Pyramid,  195 

Negative  Tertiary  Rhombohe- 
dron,  96-98,  198 

Negative  Tetragonal  Scaleno- 
hedron, 195 

Negative  Tetragonal  Triakis 
Tetrahedron,  124,  132,  133, 
183,  185 

Negative  Tetragonal  Trapezo- 
hedron, 69,  196 

Negative  Tetrahedral  Penta- 
gonal Dodecahedron,  125, 
140,  141,  184 

Negative  Tetrahedron,  124, 
132,  183,  185 

Negative  Trigonal  Triakis  Te- 
trahedron, 124,  134,  183,  185 

Negative  Trigonal  Trapezohe- 
dron, 98,  100,  199 


Nephelite  Type,  74,  76,  81,  103, 

104,  109,  121,  165,  180,  181, 

222 
Nephelite   Type,   Symmetry  of, 

106,  165,  260 
Nicknames   in   Crystallography, 

1*8-202 

Niter,  3,  51,  57,  204,  214  j 

Nomenclature,   Crystallographic 

187-202 

Nomenclature,  Hexagonal,  75 
Nomenclature,    Isometric,    122, 

123 

Nomenclature,  Monoclinic,  41-43 
Nomenclature,  Orthorhombio 

50,  51 

Nomenclature,  Tetragonal  60-62 
Nomenclature,  Triclinic,  10-13 
Normal  Class,  Monoclinic,  170, 

208-211,  258  » 

Normal  Group,    168,   182,   183, 

205,  206,  258 
Normal    Group,    Orthorhombic, 

171,  172,  259 
Normal      Group,       Tetragonal, 

175,  176 
Normal    Rhombohedral    Group, 

179 

Oblique    Angled    Quadralateral 

Prism,  190 
Oblique  Axis,  42 
Oblique  Hemihedral  Class,  185, 

186 
Oblique      Hemihedral      Forms, 

124,    131-135,    141-144,    165, 

185,   186,   236,   237,  242-244, 

253,  254 
Oblique      Hemihedral      Forms, 

Symmetry  of,  123,  135,  165, 

261 


282 


INDEX. 


Oblique  Hemihedral  Forms  in 
combination,  141 

Oblique  Ehombic  Prism,  190 

Obtuse  Khombohedron,  87 

Octagonal  Prism,  191 

Octahedral  Axes,  131,  135,  139 

Octahedral  Cleavage,  155,  159 

Octahedrite,  61,  62,  70,  73,  74, 
218 

Octahedron,  3,  12,  13,  14,  22, 
23,  42-45,  51,  54,  123,  128, 
132,  141,  143,  184,  186,  188, 
189,  200,  204,  207,  236,  239- 
242,  245-247,  253,  254 

Octahedron,  Distorted,  3,  26, 
204,  254 

Octahedron,  Hexakis,  124,  130, 
137,  144,  186,  188,  201,  207, 
236-239,  241,  242 

Octahedral  Pyramidal  Icosi 
Tetrahedron,  200 

Octahedron,  Tetragonal  Triakis 
124,  129,  141-144,  201,  236, 
237,  240-242,  244-246 

Octahedral  Trigonal  Icosi  Te- 
trahedron, 200 

Octahedron,  Trigonal  Triakis, 
124,  128,  129,  133,  134,  141- 
143,  188,  200,  207,  236-237, 
240 

Octakis  Hexahedron,  201 

Octants,  7 

Optical  Mineralogy,  2 

Organic  World,   1 

Ortho-Axis,  42 

Orthoclase,  149,  150,  152,  153, 
249,  250,  255 

Ortho-Diagonal,  42 

Ortho-Dome,  43,  44 

Ortho-Pinacoidal  Cleavage,  155- 
157 


Ortho-Pinacoid,  3,  11,  12,  15, 17, 

18,  26,  41,  43,  44,  46,  47,  50, 

51,  54,  203 

Orthorhombie  Axes,  7, 50, 57,  203 
Orthorhombic     and     Hexagonal 

Crystals,  Distinction  between, 

52 
Orthorhombic      and      Isometric 

Crystals,  Distinction  between, 

51,  52 
Orthorhombic  Brachy-Dome,  50, 

.  51,  54,  190 
Orthorhombic  Brachy-Pinacoids, 

50,  54 
Orthorhombic     Brachy     Prism, 

190 

Orthorhombic  Cleavage,  157 
Orthorhombic    Crystals,    Direc- 
tions for  Studying,  59 
Orthorhombic   Crystals,    Distin- 
guishing   Characteristics    of, 

53,  54 
Orthorhombic  Crystals,  Beading 

Drawings  of,  57,  58 
Orthorhombic  Forms,  58 
Ogdohedral  Class,  176,  177 
Ogdomorphous  Class,  176,  177 
Orthorhombic  Hemihedral 

Forms,  55,  56,  162,  163,  170, 

171,  259 
Orthorhombic          Hemimorphic 

Forms,    51,    52,    56,    57,    163, 

171,  259 
Orthorhombic  Hemihedral 

Forms,  Symmetry  of,  55,  162, 

163,   259 
Orthorhombic          Hemimorphic 

Forms,  Symmetry  of,  56,  163, 

259 
Orthorhombic    Hemi    Pyramid, 

194 


INDEX. 


283 


OrtliorhombiCjHolohedral  Forms, 

54,  55,  162,  171,  172,  259 
OrthorhombiCjHolohedralForms, 

Symmetry  of,  23,    51,    52,    55, 

162,  259 
Orthorhombic  Macro-Domes,  50, 

51,  54,  lyl 
Orthorhombic   Macro-Pinacoids, 

50,  54 

Orthorhombic  Macro-Prism,  191 
Orthorhombic  Nomenclature,  50, 

51 

Orthorhombic  Notation,  58 
Orthorhombic  Octahedron,  194 
Orthorhombic  Pinacoid,  50,  54, 

171,  203 
Orthorhombic  Planes,  Rules  for 

naming,  54 
Orthorhombic  Prism,  50,  51,  54, 

171 
Orthorhombic    Pyramid,    7,    25, 

51,  54,  171,  172,  194 
Orthorhombic  Shorthand  or  No- 
tation, 58 

Orthorhombic  Sphenoid,  55,  56, 

66,  171,  194,  215,  216 
Orthorhombic     Symmetry,     23, 

51,  52,  55,  56,  59, 162, 163,  259 
Orthorhombic  System,  7,  50-59, 

162,   163,    170-172,   203,   204, 

211-216,   247,   250,   252,   256- 

259 
Orthorhombic    Vertical    Dome, 

190 
Orthorhombic    Vertical    Prism, 

190 

Orthotype,  194 
Oscillatory     Combination,     151, 

247 

Parallel    Groups,    3,    149,    150, 
204,  205,  247 


Parallel  Growths,  149,  150,  247 
Parallel       Hemihedral       Class, 

184,  185 
Parallel      Hemihedral      Forms, 

125,    135-138,    141-144,    166, 

200-202,   207,   215,  237,   238, 

244-246,  254 
Parallel   Hemihedral   Forms   in 

combination,  141 
Parallel      Hemihedral       Forms 

Symmetry    of,    51,    52,    123, 

138,  166,  261 

Parallel  Eock  Jointing,  360 
Parameters,  31-33,  75 
Parameters    of    the    Secondary 

Hexagonal   Prism  and  Pyra- 
mid, 83,  84 

Parsons,  C.  L.,  x,  167,  173 
Parting  Planes,  159,  160 
Parting   Plane    Shorthand,    159 
Partings,  159,  160 
Patton,  H.  B.,  vi 
Penetration      Twins,      151-153, 

253-257 

Penfield,  S.  L.,  x,  167 
Pentagonal    Dodecahedron,    24, 

25,  51,  52,  125,  135-138,  142, 

143,  183,  185,  200,  207,  237, 

238,  244-246,  254 
Pentagonal  Dodecahedron,  Sym- 
metry  of,  51,  52, 138, 166,  261 
Pentagonal    Hemihedral    Class, 

184,  185 
Pentagonal          Icositetrahedral 

Class,  184 
Pentagonal  Icositetrahedron,123, 

125,  138,  139,  142,  144,  166, 

184,  202,  238,  261 
Pentagonal  Icositetrahedrons  in 

combination  with  other  forms. 

142 


284 


INDEX. 


Pentagonal       Icositetrahedrons 

Symmetry  of,  139,  166,  261 
Pentagonal    Tetrahedral    Dode- 
cahedron,   123,   125,    140-142, 
144,  166,  183,  184,  202,  238, 
239,  261 

Pedial  Class,  167,  261 
Pedion,  168-171 
Pedion,  First,  168,  170 
Pedion,  Primary,  168 
Pedion,  Second,  168,  169 
Pedion,   Secondary,  168,   170 
Pedion,  Third,  168,  170,  171 
Pedion,  Tertiary,  168 
Pedion,  Quaternary,  168 
Phillipsite,   149,  150,  153,  154, 

255,  258 

Pinacoid,  11,  12,  13,  42,  44,  50, 
54,  60,  63,   80,  104,  168-183, 
188,  199,  200,  203,  205 
Pinacoidal  Class,  168,  169,  205, 

206,  258 

Pinacoidal  Cleavage,  155-158 
Pinacoid,  Basal,  11,  21,  42,  44, 

60,  63,  80,  104,  172-183,  199 
Pinacoid,  First,  168-171 
Pinacoid,  Hexagonal  76, 176-183 
Pinacoid,    Macro,    12,    21,    54, 

200,  205 

Pinacoid,  Primary,  169 
Pinacoid,  Quaternary,  169 
Pinacoid,  Second,  168,  170,  171 
Pinacoid,  Secondary,  169,  170 
Pinacoid,  Tertiary,  169 
Pinacoid,  Third,  169-171 
Pinacoid,   Vertical,   11,   21,  42, 

44,  199 

Plagihedral  Group,  184 
Plagihedral    Hemihedral    Class, 

184 
Plagihedral  Hemihedral  Forms, 


123,  125,  138,  139,  142,  144, 
166,  184,  202,  238,  261 

Plagiohedron,  199 

Plane  of  Symmetry,  15-18,  23- 
25,  39,  40,  41,  44,  46,  49,  51- 
56,  59,  64,  67-69,  72,  74,  84, 
90,  93,  94,  96,  98,  100,  102, 
103,  121,  130,  131,  135,  138, 
139,  141,  147,  161-166,  168, 
169,  172,  173,  175,  203,  258- 
261 

Planes  of  Symmetry,  how  rep- 
resented, 161 

Planes,  relation  to  Axes,  43,  51, 
62,  75 

Planes,  relation  to  Hexagonal 
Axes,  75 

Planes,  Eules  for  naming  them 
in  the  Hexagonal  System, 
104-109 

Planes,  Variation  of  Crystal 
Planes,  3 

Poland,  187 

Polarized   Light,    150 

Polynomial  Names,  188 

Polysynthetic  Twinning,  151, 
153,  247 

Popular  Science  Monthly,  viii 

Position  Ditrigonal  Prism,  98, 
99,  192 

Positive  Ditrigonal  Pyramid, 
95,  96,  199 

Positive  Dyakis  Dodecahedron, 
51,  125,  135,  137,  138,  215 

Positive  Forms,  36 

Positive  Hexagonal  Scaleno- 
hedron,  89,  197 

Positive  Hexagonal  Semi-axes, 
109,  110 

Positive  Hexagonal  Trapezo- 
hedron,  9rf,  94 


INDEX. 


285 


Positive  Hexakis  Tetrahedron, 
124,  135,  186 

Positive  Left-Handed  Tertiary 
Bhombohedron,  198 

Positive  Left-Handed  Tertiary 
Trigonal  Prism,  193 

Positive  Left-handed  Tertiary 
Trigonal  Pyramid,  199 

Positive  Left-handed  Trigonal 
Trapezohedron,  25,  76,  100, 
104,  199,  207 

Positive  or  Eight-Handed  Hex- 
agonal Prism,  192 

Positive  or  Eight-Handed  Or- 
thorhombic  Sphenoid,  194 

Positive  or  Eight-Handed  Ter- 
tiary Hexagonal  Pyramid, 
198 

Positive  or  Eight-handed  Tetra- 
gonal Trapezohedron,  196 

Positive  or  Eight-Handed  Tri- 
gonal Prism,  192 

Positive  or  Eight-Handed  Tri- 
gonal Pyramid,  197 

Positive  Pentagonal  Dodeca- 
hedron, 125,  136,  137,  185,^ 
207 

Positive  Primary  Trigonal 
Priam,  101,  176,  192 

Positive  Primary  Trigonal 
Pyramid,  101,  102 

Positive  Ehombohedron,  85,  87, 
88,  198 

Positive  Bhombohedron  of  the 
Second  Order,  197 

Positive  Eight-Handed  Tertiary 
Trigonal  Prism,  193 

Positive  Eight-handed  Tertiary 
Trigonal  Pyramid,  199 

Positive  Eight -handed  Trigonal 
Trapezohedron,  25,  76,  100, 
104,  199,  207 


Positive  Eight-handed  Tertiary 
Ehombohedron,  i98 

Positive  Scalenohedron,  197 

Positive  Secondary  Ehombo- 
hedron, 96,  97,  197 

Positive  Secondary  Trigonal 
Prism,  98,  99,  176,  192 

Positive  Secondary  Trigonal 
Pyramid,  98-100,  197 

Positive  Sphenoid,  56,  195 

Positive  Tertiary  Hexagonal 
Pyramid,  91-93,  198 

Positive  Tertiary  Hexagonal 
Prism,  91-93,  192 

Positive  Tertiary  Pyramid,  195 

Positive  Tertiary  Ehombohe- 
dron, 96-98,  198 

Positive  Tertiary  Trigonal 
Prism,  101,  102,  193 

Positive  Tertiary  Trigonal 
Pyramid,  101,  102,  199 

Positive  Tetrahedral  Penta- 
gonal Dodecahedron,  125,  140, 
141,  184 

Positive  Tetrahedron,  124,  132, 
183,  185 

Positive  Tetragonal  Scalenohe- 
dron, 195 

Positive  Tetragonal  Trapezohe- 
dron, 69,  196 

Positive  Tetragonal  Triakis  Te- 
trahedron, 124,  132,  133, 
183,  185 

Positive  Trigonal  Trapezohe- 
dron, 25,  76,  98,  100,  104, 
199,  207 

Positive  Trigonal  Triakis  Tetra- 
hedron, 124,  134,  183,  185 

Primary  and  Secondary  Tetra- 
gonal Prisms,  Distinction  be- 
tween, 64 


286 


INDEX. 


Primary   and  Secondary  Hexa- 
gonal   Prisms,    Eelations    to 

each  other,  82,  83 
Primary  and  Secondary  Tetra- 
gonal   Pyramids,    Distinction 

between,  65 

Primary  Di  Trigonal  Prism,  192 
Primary  Hexagonal  Prism,  80- 

85,    91,    101,    104,    177,    179- 

183,  191 
Primary    Hexagonal    Pyramid, 

81-85,  93,   102,  106,  181-183, 

188,  196 

Primary  Pyramid,  194,  204 
Primary      Khombohedron,      18, 

26,  27,  74,  76,  81,  87,  88,  104, 

204,  207 
Primary  Tetragonal  Prism,  61, 

63,  175,  176,  191 
Primary    Tetragonal    Pyramid, 

61,  63,  175,  176,  194 
Primary    Tetragonal  Pyramids, 

Number  of,  65 
Primary    Trigonal   Prism,    101, 

105,  176,  178-180,  192 
Primary  Trigonal  Pyramid,  101, 

102,  106,  177-180,  196 
Principal  Khombohedron,  87 
Prism,  12,  13,  21,  22,  43,  44,  50, 

54,  61,  63,  64,  67,  68,  76-83, 

91-93,    98,    99,    101-106,    108, 

109,  170-183,  188-193,  203 
Prismatic  Class,  170 
Prismatic  Cleavage,  155-158 
Prism,  Dihexagonal,   81-85,   99, 

101,  105,  179,  181-183,  192 
Prism,  Ditetragonal,  61,  63,  98, 

99,  174,  191 
Prism,  Ditrigonal,  98,  99,  105, 

177,  179,  180,  192 
Prism,  Hemi  Ditetragonal,    67, 

191 


Prism,  Hexagonal  of  the  First 
Order,  80-85,  90,  101,  104, 
177,  179-183,  191 

Prism,  Hexagonal  of  the  Second 
Order  81-85,  91,  93,  99,  101, 
105,  177,  179-183,  192 

Prism,  Hexagonal  of  the  Third 
Order,  91,  92,  105,  181,  182, 
192 

Prism,  Monoclinic,  43,  44,  170, 
190,  203 

Prism  of  the  First  Order,  191 

Prism  of  the  Second  Order,  191 

Prism  of  the  Third  Order,  Te- 
tragonal, 67,  68,  175,  191 

Prism,  Parameters  of  the  Secon- 
dary Hexagonal,  83,  84 

Prism,  Primary,  170-174,  191 

Prism,  Primary  Hexagonal,  80- 
85,  91,  101,  104,  177,  179- 
183,  191,  204 

Prism,      Primary,      Monoclinic, 

170,  190 

Prism,   Primary,   Orthorhombic, 

171 
Prism,  Primary,  Tetragonal,  61, 

63,  175,  176,  191 
Prism,   Primary  Trigonal,   101, 

105,  176,  178-180,  192 
Prism,  Quaternary,  170 
Prism,     Secondary    Hexagonal, 

81-85,   91,   93,   99,   101,    105, 

177,  179-183,  192 
Prism,    Secondary,    Orthorhom- 
bic, 171 
Prism,  Secondary  Trigonal,  98, 

99,  105,  176-178,  192 
Prism,   Tertiary,   170-173,   191 
Prism,  Tertiary  Hexagonal,  91, 

92,  105,  181,  182,  192 
Prism,   Tertiary,  Orthorhombic, 

171,  1/2 


INDEX. 


287 


Prism,  Tertiary  Tetragonal,  67, 

68,  175,  191 
Prism,   Tertiary   Trigonal,   101, 

102,  106,  177,  178,  193 
Prism  Tribe,  189-193 
Pseudo-hemimorphic  Form,  46 
Pseudomorphs,  148 
Pyramid,  12,  13,  22,  42,  43,  45, 

51,  54,  61-63,  65,  67,  68,  76- 

79,  81-83,   85,  88,  91-93,  95, 

96,     98-103,     106-109,      121, 

172-183,    188,    189,    193-199, 

204 
Pyramid,   Dihexagonal,   82,   93, 

101,  107,  182,  183,  197 
Pyramid,  Ditetragonal,   62,  63, 

121,  175,  176,  195,  206 
Pyramid,    Ditrigonal,     95,    96, 

107,  179,  180,  198 
Pyramid,  Hemi-Ditetragonal  67, 

68,  195,  196 
Pyramid,     Hexagonal     of     the 

First  Order,   81-85,  93,    102, 

106,  181-183,  188,  196 
Pyramid,     Hexagonal     of     the 

Second  Order,  82-85,  96,  106, 

179-183,  196,  197 
Pyramid,     Hexagonal     of     the 

Third  Order,  91-93,  181,  182, 

198 
Pyramid,  Hexagonal,   Tertiary, 

91-93,  181,  182,  198 
Pyramid  Octahedron,  124,  128, 

129,  141-143,  200 
Pyramid  of  the  Diametral  Or- 
der, 19o 

Pyramid  of  the  First  Order,  194 
Pyramid    of    the    First    Order, 

Tetragonal,  61,  63,  175,  176, 

194 
Pyramid  of  the  Second  Order, 

195 


Pyramid   of   the    Third   Order, 

195 
Pyramid   of   the   Third  Order, 

Tetragonal,  67,  68,  175,  195 
Pyramid  of  the  Unit  Order,  194 
Pyramid,   Orthorhombic,   7,   25, 

51,   54,   71,  72,,  194 
Pyramid,    Parameters    of    the 

Secondary  Hexagonal,  83,  84 
Pyramid,  Primary,  173,  174 
Pyramid,    Primary    Hexagonal, 

81-85,  93,  102,  106,  181-183, 

188,  196 
Pyramid,    Primary   Tetragonal, 

61,  63,  175,  176,  194 
Pyramid,      Primary      Trigonal, 

101,  102,  106,  1/7-180,  196 
Pyramid,  Quaternary,  171 
Pyramid,  Secondary,  173,  174 
Pyramid,  Secondary  Hexagonal, 
82-85,  96, 106, 179-183, 196, 197 
Pyramid,  Secondary  Tetragonal, 

61,  63,  175,  176,  19o 
Pyramid,    Secondary    Trigonal, 

98-100,  107,  177,  178,  197 
Pyramid,  Tertiary,  173 
Pyramid,    Tertiary   Tetragonal, 

67,  68,  175,  195 
Pyramid,      Tertiary      Trigonal, 

101,  102,  108,  177,  178,  199 
Pyramid  Tetrahedron,  124,  133, 
134,  142,  144,  183,  185,  201 
Pyramid  Tribe,  19^-200 
Pyramidal  Class,  Orthorhombic, 

171,  259 

Pyramidal     Class,     Tetragonal, 

172,  173 

Pyramidal  Cleavage,  155-158 
Pyramidal  Cube,  200 
Pyramidal  Dodecahedron,  201 
Pyramidal  Garnetohedron,  201 
Pyramidal  Group,  181,  182 


288 


INDEX. 


Pyramidal    Group,    Tetragonal, 

174,   175 
Pyramidal     Hemihedral     Class, 

Tetragonal,     174,     175,     181, 

182,  259 
Pyramidal  Hemimorphie   Class, 

Tetragonal,     172,     173,    180, 

181,  261 
Pyramidal     Hexagonal     Group, 

91-93,  121,  164,  260 
Pyramidal  Hexagonal,   Symme- 
try of,  93,  164,  260 
Pyramidal     Tetragonal    Group, 

67-69,  174,  175 
Pyramidal     Tetragonal     Group 

Symmetry  of,  68,  69,  163 
Pyramidal  Tetrahedron,  201 
Pyrite,  24,  25,  51,  123,  125,  135- 

137,  148-150,  153,  207 
Pyrite  Dodecahedron,  200 
Pyritohedral  Group,  184,  185 
Pyritohedral  Hemihedral  Group, 

184,  185 

Pyritohedron,    24,    25,    51,    52, 
125,   135-138,   142,   143,   183, 

185,  200,  207,  237,  238,  244- 
246,  254 

Pyritohedron,      Symmetry      of, 

51,  52 

Pyritoid,  200 
Pyroxene,  41-44,  46,  47 

Quadratic  Octahedron,  194,  195 
Quadratic    Octahedron    of    the 

First  Order,  194 
Quadratic    Octahedron    of    the 

First  Series,  194 
Quadratic    Octahedron    of    the 

Second  Series,  195 
Quadratic  rrism,  191 
Quadratic  Pyramid,  195 


Quadratic  Tetrahedron,  194 
Quartz,  3,  18,  26,  74,  76,  81,  83, 

87,    100,   104,   149,   150,   153, 

204-206,  233,  234,  255 
Quartzoid,   196,   197 
Quartzoid   of   the   First   Order, 

196 
Quartzoid  of  the  Second  Order, 

197 

Reading  Drawings  of  Hexagonal 
Crystals,  109-113 

Beading  Drawings  of  Isometric 
Crystals,  145-157 

Reading  Drawings  of  Ortho- 
rhombic  Crystals,  57,  58 

Reading  Drawings  of  Tetra- 
gonal Crystals,  69,  70 

Reading  Drawings  of  Triclinic 
Crystals,  30-34 

Reading  Drawings  of  Mono- 
clinic  Crystals,  46,  47 

Red  Angus,  188 

Re-entrant  Angles,  150,  256-258 

Regular  Four-sided  Double 
Pyramid,  200 

Regular  Hexagonal  Prism,  191, 
192 

Regular  Octahedron,  200 

Regular  Rhombic  Dodecahedron 
200 

Regular  Tetrahedron,  200 

Relation  of  Primary  and  Secon- 
dary Hexagonal  Prism  or 
Pyramid  to  each  other,  82,  83 

Replacement,  26,  27 

Rhombic  Dodecahedron,  123, 
126,  127,  141-143,  183-186, 
200,  204,  207,  236,  239-244, 
248,  254 

Rhombic  Octahedron,  194 


INDEX. 


289 


Rhombic  Prism,  190 
Rhombic  Pyramid,  194 
Rhombic    Pyramidohedron,    194 
Rhombic  Sphenoid,  194 
Rhombic  ISphenoidohedron,   194 
Rhombic  Tetrahedron,  194 
Rhombohedral  Class,  177 
Rhombohedral     Cleavage,     155, 

158 
Rhombohedral  Division,  74,  121 

176-180 
Rhombohedral  Group,  85-91, 121, 

164,  179 

Rhombohedral    Group,    Symme- 
try of,  90,  91 
Rhombohedral  Hemihedral  Class, 

178,  179 
Rhombohedral         Hemimorphic 

Class,  176,  179 
Rhombohedral    Lateral    Angles, 

86,  87 
Rhombohedral    Lateral    Edges, 

86,  106 

Rhombohedral  Solid  Angles,  86 
Rhombohedral  System,  74,  121, 

176-180 
Rhombohedral  Terminal  Edges, 

86 
Rhombohedral        Tetartohedral 

Class,  177 
Rhombohedral        Tetartohedral 

Group,  96-98,  164 
Rhombohedral        Tetartohedral 

Group,  Symmetry  of,  98,  164, 

260 
Rhombohedral     Zigzag     Edges, 

86,  90 
Rhombohedron,   18,   26,   27,   74, 

76,    81,    85-88,    104,    106-108, 

177,  179,  189,  196,  204,  207, 

215,  226,.  229-231,  233 


Rhombohedron,  Acute,  87 
Rhombohedron,  Obtuse,  87 
Rhombohedron     of     the     First 

Order,  88,  97,  106,  177,  179, 

196 
Rhombohedron    of    the    Middle 

Edges,  90 
Rhombohedron  of  the  Principal 

Series,   196 
Rhombohedron    of    the    Second 

Order,  96-98,  107,  177,  197 
Rhombohedron     of     the     Third 

Order,  96-98,  108,  177,  198 
Rhombohedron,       Position       of 

Axes  in,  88 
Rhombohedron,      Principal      or 

Fundamental,  87,  88 
Rhombohedron,    Relation    of    a 

Positive  to  a  Negative,  87,  88 
Rhombohedron,  relation  to  the 

Scalenohedron,  90 
Rhombohedron,    Secondary,    96- 

98,  107,  177,  197 
Rhombohedron,  Subordinate,  87 
Rhombohedron,    Symmetry    of, 

52,    90,   91,   164,   259 
Rhombohedron,     Symmetry     of 

the  Secondary  and  Tertiary, 

98 
Rhombohedron,  Tertiary,  96-98, 

108,  177,  198 
Rhombohedron  of  the  Vertical 

Primary  Zone,  196 
Right -Angled  Dodecahedron,  196 
Right-handed  Ditrigonal  Prism, 

98,  99,  193 

Right-handed  Forms,  32 
Right-handed    Positive     Secon- 
dary Rhombohedron,  96,  97 
Right-handed  Positive  Tertiary 

Rhombohedron,  96-98,  198 


290 


INDEX. 


Eight-handed  Positive  Trigonal 
Pyramid,  98-100 

Right-handed  Negative  Rhombo- 
hedron,  96-98,  198 

Right-handed  Negative  Tri- 
gonal Pyramid,  98-100 

Right-handed  Secondary  Tri- 
gonal Prism,  98,  99,  176,  192 

Right-handed  Tetragonal  Trape- 
zohedron,  69,  196 

Bight-handed  Tertiary  Hexa- 
gonal Prism,  91-93,  192 

Right-handed  Tertiary  Hexa- 
gonal Pyramid,  91-93,  198 

Right-handed  Tertiary  Trigonal 
Prism,  101,  102,  193 

Right-handed  Tertiary  Trigonal 
Pyramid,  101,  102,  199 

Right-handed  Tetrahedral  Pen- 
tagonal Dodecahedron,  125, 
140,  141,  184 

Right-handed  Hexagonal  Trape- 
zohedron,  93-95,  198 

Right-handed  Pentagonal  Icosi- 
tetrahedron,  125,  138, 139, 184 

Right-handed  Sphenoid,  56 

Right-handed  Trigonal  Trape- 
zohedron,  25,  76,  98,  100,  104, 
199,  207 

Rock  Cleavage,  loO 

Rules    for    naming    Hexagonal 

Planes,  104-109 

Rules  for  naming  Monoclinic 
Planes,  44,  45 

Rules  for  naming  Orthorhombic 
Planes,  54 

Rules  for  naming  Isometric 
Planes,  142,  144 

Rules  for  naming  Tetragonal 
Planes,  62,  66 

Rules  for  naming  Triclinic 
Planes,  21,  22 


Russia,  187 

Rutile,  149,  150,  152,  153,  252 

Saw  teeth  of  the  Hexagonal 
Scalenohedron,  89,  90,  94 

Scalene  Triangles,  94 

Scalenohedral  Class,  179 

Scalenohedral  Class,  Tetragonal, 
173,  174 

iScalenohedral  Rhombohedral 
Class,  179 

Scalenohedron,  189,  197,  215 

Scalenohedron,  Hexagonal,  88- 
91,  94,  97,  100,  107,  179,  197 

Scalenohedron,  Hexagonal  Sym- 
metry of,  52  90,  91 

Scalenohedron  Negative  Hexa- 
gonal, 89,  197 

Scalenohedron,  Positive  Hexa- 
gonal, 89,  197 

Scalenohedron,  relation  to  the 
Rhombohedron,  90 

Scalenohedron  Saw  teeth,  89,  90 

Scalenohedron,  Tetragonal,  65, 
66,  89,  174,  195 

Scheelite,  40,  68,  70,  73,  221 

Schrauf,  A.,  74 

Schrauf,  Axes  of  the  Hexa- 
gonal System,  74 

Seaman,  A.  E.,  xv 

Second  Hemimorphic  Tetarto- 
hedral  Class,  178,  179 

Second  Hexagonal  Prism,  192 

Second  Horizontal  Prism,  190 

Second  Order,  Hexagonal  Prism, 
81-85,  91,  93,  99,  101,  105, 
177,  179-183,  192 

Second  Order  Hexagonal  Pyra- 
mid, 82-85,  96,  106,  179-183, 
196,  197 

Second  Order,  .  Tetragonal 
Prism  of,  61,  63,  175,  176,  191 


INDEX. 


291 


Second  Order,  Tetragonal  Pyra- 
mid of,  61,  63,  175,  176,  195 

Second  Order,  Trigonal  Prism, 
98,  99,  105,  176-1/8,  192 

Secondary  and  Primary  Tetra- 
gonal Prisms,  Distinction  be- 
tween, 64 

Secondary  and  Primary  Tetra- 
gonal Pyramids,  Distinction 
between,  65 

Secondary  Di  Trigonal  Prism, 
192,  193 

Secondary  Forms,  26 

Secondary  Hexagonal  Prism,  81- 
85,  91,  93,  99,  101,  105,  177, 
179-183,  192 

Secondary  Hexagonal  Prism 
and  Pyramid,  Parameters  of, 
83,  84 

Secondary  Hexagonal  Pyramid, 
82-85,  99,  102,  106,  179-183, 
196,  197 

Secondary  Prism,  191 

Secondary  Pyramid,  195 

Secondary    Rhombohedron,    96- 

98,  107,  177,  197 
Secondary  Bhombohedron,  Sym- 
metry of,  98 

Secondary     Tetragonal     Prism, 

61,  63,  175,  176,  191 
Secondary  Tetragonal  Pyramid, 

61,  63,  175,  176,  195 
Secondary  Tetragonal  Pyramids, 

Number  of,  65 
Secondary  Trigonal  Prism,   98, 

99,  105,  176-178,  192 
Secondary    Trigonal    Pyramid, 

98-100,  107,  177,  178,  197 
Shakespeare,  William,  188 
Shorthand,  Crystallographic,  28- 

34,  46,  47,  57,   70,   75,   109- 

113,  146,  147,  156 


Similar    Axes,    Planes,    Edges, 

and  Angles,  13,  14 
Simple  Crystals,  25 
Slaty  Cleavage,  160 
Sodalite,  149,  150,  153,  254 
Sodium-Periodate     Type,     103, 

104,  109,  165,  176,  177,  235 
Sodium-Periodate    Type,    Sym- 
metry of,  104,  165,  260 
Solid  Angles,  Rhombohedral,  86 
Sphalerite,  149,  150,  153 
Sphenoid,    55,    56,    65,    66,    69, 

169,  171,  172,  174,  189,  194, 

195,  215,  216 
Sphenoid,  Orthorhombic,  55,  56, 

66,  171,  194 

Sphenoid,  Primary,  169, 172, 174 
Sphenoid,  Quaternary,  169 
Sphenoid,  Tertiary,  169,  172 
Sphenoid,    Tetragonal,    65,    66, 

69,  172,  174,  194,  195 
Sphenoidal     Class,    Monoclinic, 

169 
Sphenoidal    Hemihedral    Class, 

180 
Sphenoidal    Hemihedral    Class, 

tetragonal,  173,  174 
Sphenoidal  Tetartohedral  Class, 

Tetragonal,  172 
Sphenoidal  Group,    Tetragonal, 

65-67,  163,  173,  174 
Sphenoidal    Tetragonal    Group, 

65-67,  163,  173,  174 
Sphenoidal  Tetartohedral  Class, 

178 

Staurolite,  149,  150,  153,  256 
Stibnite,  50,  51,  57,  212,  214 
Straight  Axis,  42 
Striations     on      Crystals      and 

Cleavage  Plates,  150, 151,  247 
Subordinate  Form,  26 
Subordinate  Rhombohedron,  87 


292 


INDEX. 


Sugar,  41-47,  169,  209 

Sulphur,  7,  25,  50,  51,  57,  203, 
213,  214 

Symmetry,  14-19,  23-25,  37,  39, 
40,  41,  44-46,  49,  51-56,  59, 
64,  67-69,  72,  74,  76,  84,  85, 

90,  91,   93,   94,   96,   98,   100, 
102-104,   130,    131,   135,    138, 
139,    141,    147,   161-166,    168, 
169,  172,  173,  175,  203,  258- 
261 

Symmetry,  Axes  of,  18,  19,  23- 
25,  44,  51-57,  59,  64,  67-69, 
72,  74,  76,  84,  85,  90,  91,  93, 
94,  96,  98,  100,  102-104,  121, 
123,  130,  131,  135,  138,  139, 
141,  147,  162-166,  258-261 

Symmetry,  Center  of,  19,  23-25, 
55,  56,  59,  64,  67,  68,  72,  85, 

91,  93,  98,  100,  121,  131,  135, 
.139,   141,   147,    162-166,   258- 

261 

Symmetry,  Center  of,  how  rep- 
resented, 162 

Symmetry,  Hexagonal  Holohe- 
dral,  84,  85,  163,  259 

Symmetry,  how  represented, 
161,  162 

Symmetry,  Number  of  Planes 
of,  15,  40 

Symmetry  of  the  Asymmetric 
Class,  168,  261 

Symmetry  of  the  Ditetragonal 
Pyramidal  Class,  175 

Symmetry  of  the  Gyroidal 
Hemihedral  Forms,  139,  166, 
261 

Symmetry  of  Hemihedral  Iso- 
metric Forms,  123,  135,  138, 
165,  166,  261 

Symmetry  of  the  lodyrite  Type, 
103,  165,  260 


Symmetry  of  Isometric  Crys- 
tals, 23,  24,  51,  52,  123,  130, 
131,  135,  138,  139,  141,  147, 
165,  166,  261 

Symmetry  of  Isometric  Holo- 
hedral  Forms,  123,  130,  131, 

165,  261 

Symmetry  of  the  Isometric  Sys- 
tem, 23,  24,  123,  130,  131, 
135,  138,  139,  141,  147,  165, 

166,  261 

Symmetry  of  the  Monoelinic 
System,  40,  41,  44,  49,  '162, 
169 

Symmetry  of  the  Nephelite 
Type,  103,  165,  260 

Symmetry  of  Oblique  Hemihe- 
dral Forms,  123,  135,  165,  261 

Symmetry  of  the  Orthorhombic 
Hemimorphic  Forms,  56,  163, 
259 

Symmetry  of  the  Orthorhombic 

System,  23,  51,  52,  55,  56,  59, 

162,  163,  259 

Symmetry  of  Parallel  Hemihe- 
dral Forms,  51,  52,  123,  138, 
166,  261 

Symmetry  of  the  Periodate 
Type,  104,  165,  260 

Symmetry  of  the  Bhombohe- 
dron  Group,  52,  90,  91,  164 

Symmetry  of  the  Ehombohedral 
Tetartohedral  Group,  98,  164, 
260 

Symmetry  of  the  Tetragonal 
Pyramidal  Group,  68,  69,  163 

Symmetry  of  the  Tetragonal 
Sphenoidal  Group,  66,  67, 

163,  173 

Symmetry  of  the  Tetrahedral 
Pentagonal  Dodecahedron, 
123,  141,  166,  261 


INDEX. 


293 


Symmetry  of  the  Tourmaline 
Type,  103,  165,  260 

Symmetry  of  the  Triclinic  Sys- 
tem, 23-25,  162,  168,  258,  261 

Symmetry  of  the  Trigonal 
Hexagonal  Group,  96, 164,  260 

Symmetry  of  the  Trigonal  Te- 
tartohedral  Group,  102,  164, 
165,  260 

Symmetry  of  the  Trigonal 
Trapezohedron,  25,  100 

Symmetry,  Plane  of,  15-18,  23- 
25,  39,  40,  41,  44,  46,  49,  51- 
56,  59,  64,  67-69,  72,  74,  84, 
90,  93,  94,  96,  98,  100,  102, 
103,  121,  130,  131,  135,  138, 
139,  141,  147,  161-166,  168, 
169,  172,  1/3,  175,  203,  258- 
261 

Symmetry  Pyramidal  Hexag- 
onal Group,  93,  164,  260 

Table  I.     Triclinic  Forms  and 

Notations,  35 
Table    II.      Monoelinic    Forms 

and    Notations,    48 
Table     III.       Orthorhombic 

Forms  and  Notations,  58 
Table    IV.     Tetragonal    Forms 

and  Notations,  71 
Table     V.      Hexagonal    Forms 

and  Notations,  114-120 
Table     VI.      Isometric     Forms 

and  Notations,  146,  147 
Tartaric  Acid,  169 
Terminal  Edges,  Ehombohedral, 

86 
Tertiary  Hexagonal  Prism,  91, 

92,  105,  181,  182,  192 
Tertiary    Hexagonal    Pyramid, 

91-93,  107,  181,  182,  198 


Tertiary  Prism,  191 
Tertiary  Pyramid,  195 
Tertiary  Ehombohedron,   96-98, 

108,  177,  198 

Tertiary  Ehombohedron  Symme- 
try of,  98 
Tertiary  Tetragonal  Prism,  67, 

68,  175,  191 
Tertiary    Tetragonal    Pyramid 

67,  68,  175,  195 
Tertiary   Trigonal   Prism,    101, 

102,  106,  177,  178,  193 
Tertiary  Trigonal  Pyramid,  101, 

102,  108,  177,  178,  199 
Tetarto    Di    Hexagonal    Prism, 

193 
Tetarto  Di  Hexagonal  Pyramid, 

198 

Tetartohedral  Class,  183,  184 
Tetartohedral  Class,  Tetragonal, 

172 
Tetartohedral  Forms,  25,  96-102, 

140,  141 
Tetartohedral  Forms,  (Symmetry 

of,  25 

Tetartohedral  Group,  183,  184 
Tetartohedral     Group,      Tetra- 
gonal, 172 
Tetartohedral  Hexagonal  Forms, 

25,  77-79,  96-102,  121 
Tetartohedral  Isometric  Forms, 

123,   125,   140-142,   144,   166, 

183,  184,  202,  238,   239,  261 
Tetartohedral  Notation,  36-38 
Tetartohedral        Ehombohedrali 

Group,  96-98,  164 
Tetartohedral        Khombohedral 

Group,  Symmetry  of,  96,  164, 

2t>0 
Tetartohedral        Trapezohedral 

Group,  Symmetry  of,  25,  100, 

164,  260 


294 


INDEX. 


Tetartohedral  Trigonal  Group 
Symmetry  of,  102,  164,  165, 
260 

Tetarto  Hexakis  Octahedron,  202 

Tetartoid,  125,  140-142,  144, 
184,  194,  202 

Tetartomorphic  Class,  180,  181 

Tetartomorphic  Class,  Tetara- 
gonal,  172,  173 

Tetragonal  Axes,  7,  60,  203 

Tetragonal  and  Hexagonal  Sys- 
tems, Distinctions  between, 
73,  74 

Tetragonal  Cleavage,  157,  158 

Tetragonal  Compound  Forms, 
69 

Tetragonal  Crystals,  Directions 
for  Studying,  72 

Tetragonal  Crystals,  Distin- 
guishing Characteristics,  62 

Tetragonal  Crystals,  Beading 
Drawings  of,  69,  70 

Tetragonal   Dodecahedron,    201 

Tetragonal  Forms,  71 

Tetragonal  Hemihedral  Forms, 
65-69,  163,  220,  221,  259 

Tetragonal  Hemihedral  Forms 
Symmetry  of,  66-69,  163,  173, 
174,  259,  261 

Tetragonal  Hemihedral  Hemi- 
morphic  Forms,  Symmetry  of, 
172,  173,  261 

Tetragonal  Hemihedral  Pyra- 
midal Group,  Symmetry  of, 

68,  69,  163,  259 
Tetragonal    Hemihedral    Sphe- 

noidal  Group,   Symmetry   of, 
66,  67,  163,  173,  174,  259 
Tetragonal   Hemihedral    Trape- 
zohedral  Group,  Symmetry  of, 

69,  163,  259 


Tetragonal    Holohedral    Forms, 

63-65,  163,  216-220,  259 
Tetragonal    Holohedral    Forms, 
Symmetry  of  64,  74,  163,  172, 
259,  261 

Tetragonal    Holohedral    Hemi- 
morphic  Forms,  Symmetry  of, 
175,  261 
Tetragonal    Icosi    Tetrahedron, 

201 

Tetragonal  Notation,  71 
Tetragonal     Parallel     Growths, 

3,  149,  205 
Tetragonal    Planes,    Rules    for 

naming,  62,  63 

Tetragonal  Primary  and  Secon- 
dary Prisms,  Distinction  be- 
tween, 64 

Tetragonal  Primary  and  Secon- 
dary    Pyramids,     Distinction 
between,  65 
Tetragonal  Prism  of  the  First 

Order,  61,  63,  175,  176,  191 
Tetragonal  Prism  of  the  Second 

Order,  61,  63,  175,  176,  191 
Tetragonal  Prism  of  the  Third 

Order,  67,  68,  175,  191 
Tetragonal    Pyramidal     Group, 

67-69,  174,  175 
Tetragonal    Pyramidal    Group, 

Symmetry  of,  68,  69 
Tetragonal     Pyramid     of     the 
First  Order,  61,  63,  175,  176, 
194 

Tetragonal     Pyramid     of     the 
Second    Order,    61,    63,    175, 
176,  195 
Tetragonal  Pyramidohedron  of 

the  First  Direction,  194 
Tetragonal  Pyramidohedron   of 
the   Second   Direction,    195 


INDEX. 


295 


Tetragonal     Pyramid     of     the 

Third  Order,  67,  68,  175,  195 

Tetragonal    Scalenohedron,    65, 

66,  89,  174,  195 
Tetragonal    Sphenoid,    65,    66, 

69,  172,  174,  194,  195 

Tetragonal  Shorthand  or  Nota- 
tion, 71 

Tetragonal  Sphenoidal  Group 
Symmetry  of,  66,  67,  163,  173 

Tetragonal  System,  7,  60-72, 
149,  163,  172-176,  203,  205, 
206,  216-221,  224,  225,  251, 
253,  259,  261 

Tetragonal  System,  Symmetry 
of,  64,  67,  69,  74,  163,  172- 
175,  259,  261 

Tetragonal  Tertiary  Prism,  67, 
68,  175,  191 

Tetragonal    Tertiary    Pyramid, 

67,  68,  175,  195 
Tetragonal  Tetartohedral 

Forms,  Symmetry  of,  172,  261 
Tetragonal  Trapezohedral 

Group,  69,  163,  174 
Tetragonal  Trapezohedron,  Sym- 
metry of,  69,  163 
Tetragonal  Triakis  Octahedron, 

124,    129,    141-144,   201,    236, 

237,  240-242,  244-246 
Tetragonal  Triakis  Tetrahedron, 

124,  132,  133,  142,  143,  183, 

185,  200,  237,  244 
Tetragonal  Tristetrahedron,  124, 

132,  133,  142,  143,  183,  185, 

200,    237,    244 
Tetrahedral  Group,  185,  186 
Tetrahedral    Hemihedral    Class, 

185,  186 
Tetrahedral   Hemihedral    Class, 

Tetragonal,  173,  174 


Tetrahedron,  Hexakis,  124,  134, 
135,  140,  144,  186,  201,  237, 
244,  261 

Tetrahedral  Isometric  Forms, 
Symmetry  of,  123,  141,  166, 
261 

Tetrahedral  Pentagonal  Dode- 
cahedral  Class,  183,  184 

Tetrahedral  Pentagonal  Dode- 
cahedron, 123,  125,  140-142, 
144,  166,  183,  184,  202,  238, 

239,  261. 

Tetrahedral  Pentagonal  Dode- 
cahedrons in  combination  with 
other  forms,  142 

Tetrahedral  Pentagonal  Dode- 
cahedron, Symmetry  of,  123, 
141,  166,  261 

Tetrahedral  Trigonal  Icosi  Te- 
trahedron, 201 

Tetrahedral  Tetartohedral 

Class,  172 

Tetrahedrite,  149,  150,  153,  254 

Tetrahedron,  124,  132,  142,  143, 
183,  185,  200,  236,  237,  242 

Tetrahedron,  Tetragonal,  Tria- 
kis, 124,  132,  133,  142,  143, 
183,  185,  200,  237,  244 

Tetrahedron,  Trigonal  Triakis, 
124,  133,  134,  142,  144,  183, 

185,  201 
Tetrahexahedron,  123,  127,  128, 

135,  136,  141-143,  184-186, 
200,  208,  236-238,  240,  244, 
248 

Tetrakis  Hexahedron,  123,  127, 
128,  135,  136,  141-143,  184- 

186,  189,   200,   208,   236-238, 

240,  244,  248 

The  Pennsylvania  State  Col- 
lege, vii 


296 


INDEX. 


Third  Order,  Hexagonal  Prism, 

91,  92,  105,  181,  182,  192 
Third  Order,  Tetragonal  Prism, 

67,  68,  175,  191 
Third  Order,  Tetragonal  Pyra- 
mid, 67,  68,  1/5,  195 
Topaz,  50,  51 
Tourmaline   Type,   74,   76,   108, 

104,  109,  165,  178,  179,  230, 

235 
Tourmaline  Type,  Symmetry  of, 

103,  165,  260 
Trapeziums,  94,  137 
Trapezohedral  Class,  181 
Trapezohedral  Group,  177,  178, 

181 
Trapezohedral  Hemihedral 

Class,  181 
Trapezohedral  Hexagonal 

Group,  93-95,  164 
Trapezohedral  Hexagonal 

Group,  Symmetry  of,  94,  164, 

260 
Trapezohedral        Tetartohedral 

Group,  98-100,  164,  177,  178 
Trapezohedral        Tetartohedral 

Class,  177,  178 
Trapezohedral        Tetartohedral 

Group,  Symmetry  of,  25,  100, 

164,  260 
Trapezohedral  Tetragonal 

Group,  69,  163 
Trapezohedron,    124,    129,    141- 

144,  189,  201,  207,  236,  237, 

240-242,  244-246 
Trapezohedron,  Hexagonal,  93- 

95,  107,  121,  181,  198,  221 
Trapezohedron,  Hexagonal,  Sym- 
metry of,  94 
Trapezohedron,         Left-handed 

Hexagonal,    93-95,    198 


Trapezohedron,  Negative  Hexa- 
gonal, 93,  94 

Trapezohedron,  Positive  Hexa- 
gonal, 93,  94 

Trapezohedron,  Bight-handed 
Hexagonal,  93-95,  198 

Trapezohedron,  Tetragonal,  69, 
174,  196 

Trapezohedron,  Tetragonal,  Sym- 
metry of,  69 

Trapezohedron  Trigonal,  25, 
74,  76,  98,  100,  104,  108,  178, 
207 

Trapezoidal  Dodecahedron,  201 

Trapezoidal  Icosi  Tetrahedron, 
201 

Trapezoid  Di  Dodehedron,  201 

Trapezoid  Di  Hexahedron,  198 

Trapezoid  Icosi  Tetrahedron,  201 

Trapezoid  Tetrahedron,  200 

Triakis  Octahedron,  124,  128, 
129,  133,  134,  141-143,  200, 
207,  236,  237,  240 

Triakis  Tetrahedron,  124,  133, 
134,  142,  144,  183,  185,  201, 
237,  242-244,  261 

Tribe,  Isometric,  189,  200-202 

Tribe,  Prism,  189-193 

Tribe,  Pyramid,  193-200 

Triclinic  Axes,  7,  9,  10,  29,  33, 
203 

Triclinic  Cleavage,  156 

Triclinic  Crystals,  Directions, 
for  Studying,  38,  39 

Triclinic  Crystals,  Distinguish- 
ing Characteristics  of,  19-21 

Triclinie  Crystals,  Obliquity  of 
Angles  of,  20,  21 

Triclinic  Crystals,  Beading 
Drawings  <  x,  30-34 


INDEX. 


297 


Triclinic  Domes,  21,  22 

Trj clinic  Forms,  35 

Triclinic    Henri    Brachy    Dome, 

190 
Triclinic   Hemi   Brachy   Prism, 

190 
Triclinic      Hemihedral      Class, 

167,  261 
Triclinic     Hemihedral      Forms,    I 

24,  25,  167,  168,  257,  258 
Triclinic     Hemihedral     Forms, 

Symmetry  of,  168,  261 
Triclinic    Hemi    Macro    Dome, 

190 
Triclinic    Hemi    Macro    Prism, 

190 
Triclinic  Hemi  Vertical  Dome, 

189 
Triclinic  Hemi  Vertical  Prism, 

189 
Triclinic      Holohedral      Forms, 

23,  162,   168,   169,   205,  206, 

258 
Triclinie     Holohedral      Forms, 

Symmetry  of,  23-25,  162,  258 
Triclinie  Notation,  35 
Triclinic  Pedion,  168 
Triclinic  Pinacoids,  12,  13,  19- 

21,  25,  26,  33,  34,  44,  200,  205 
Triclinic     Planes,     Eules     for 

naming,  21,  22 
Triclinic  Prism,  21,  22 
Triclinic  Pyramid,  12,  13,  19-21, 

25,  26,  33-35,  44,  193,  205 
Triclinic    Shorthand    or    Nota- 
tion, 35 

Triclinic  System,  7,  9-39,  44, 
162,  167-169,  203,  205,  206. 
247,  249,  258,  261 

Triclinic  System,  Symmetry  of, 
23-25,  162,  168,  258,  261 


Triclinic   Tetartohedral   Forms. 

25 
Triclinic   Tetarto   Pyramid,   13, 

19-21,    25,    26,    33,    34,    44, 

193,  205 

Triclinohedral  Prism,  189 
Trigonal     Bipyramidal      Class, 

178 
Trigonal  Division,  74,  121,  176 

180 

Trigonal  Dodecahedron,  201 
Trigon-Dodecahedron,  124,  133, 

134,  142,  144,  183,  185,  201 
Trigonal  Group,  178 
Trigonai  Hexagonal  Group,  95, 

96,  164 
Trigonal      Hexagonal      Group, 

Symmetry  of,  96,  164,  260 
Trigonal  Hemihedrai  Class,  180 
Trigonal  Icosi  Tetrahedron,  201 
Trigonal  Polyhedron,  201 
Trigonal  Prism,  189,  192 
Trigonal    Prism    of    the    First 

Order,    101,    105,    176,    178- 

180,  192 
Trigonal   Prism,   Primary,   101, 

105,  176,  178-180,  192 
Trigonal  Prism   of  the   Second 

Order,   98,   99,    105,   176-178, 

192 
Trigonal    Prism    of    the    Third 

Order,  101,  102,  106,  177,  178, 

193 
Trigonal  Prism,  Secondary,  98, 

99,  105,  176-178,  192 
Trigonal  Prism,   Tertiary,  101, 

102,  106,  177,  178,  193 
Trigonal  Pyramidal  Class,  176, 

177 
Trigonal  Pyramid  of  the  First 

Order,  101,  102,  106,  177-180, 

1UU 


298 


INDEX. 


Trigonal  Pyramid,  Frimary,  101, 

lOiS,  106,  177-180,  196 
Trigonal      Pyramid      of      the 

Second    Order,    98-100,    107, 

IV  7,  1/8,  195,  197 
Trigonal  Pyramid  of  the  Third 

Order,    101,    102,    108,    177, 

178,  199 
Trigonal    Pyramid,    Secondary, 

98-100,  107,  177,  178,  197 
Trigonal     Pyramid,      Tertiary, 

101,  102,  108,  177,  178,  199 
Trigonal    Khombohedral    Class, 

177 
Trigonal  Symmetry,  Axis,  how 

represented,  162 
Trigonal  System,  74 
Trigonal     Trapezohedron,     25, 

74,  76,  98,  100,  104,  108,  178, 

207 
Trigonal    Tetartohedral    Class, 

177,  178 
Trigonal   Tetartohedral   Group, 

101,  102,  164,  165 
Trigonal   Tetartohedral    Group, 

Symmetry  of,  102,  164,  165, 

260 
Trigonal    Trapezohedral    Class, 

177,   178 

Trigon  Trapezohedron,  199 
Trigonal     Triakis    Octahedron, 
.      12*,  128,  129,  133,  134,  141- 

143,   188,   200,   207,   236-237, 

240 
Trigonal    Triakis    Tetrahedron, 

124,  133,  134,  142,  144,  183, 

185,  201,  237,  242-244,  261 
Trigonal   Tristetrahedron,    124, 
133,  134,  142,  144,  183,  185, 

201 

Trigonotype  Hemihedral  Class^ 
179,  180 


Trillings,   152,  256 
Trinomial  Names,  188 
Tripyramidal  Group,  181,  182 
Tri-rhombohedral  Group,  177 
Trisoctahedron,    124,    128,    129, 

333,  134,  141-143,  200 
Tristetrahedron,   124,  132,   133, 

142,  143,  183,  185,  201,  237, 

242-244,  261 
Truncation,  27 
Twelve-sided  Prism,  192 
Twin,  149-154,  247-258 
Twin,    Contact,    151-153,    247- 

253,  257 

Twin,  Cyclic,  153,  252,  253 
Twin,      Penetration,      151-153, 

253-256,  257,  258 
Twinned  Crystals,  150-154,  247- 

258 

Twinning  Axis,  152 
Twinning  Plane,   152,   247-253, 

257 
Twinning,    Polysynthetic,    151, 

153,  247 
Type,  lodyrite,  74,  76,  81,  102- 

104,  108,  121,  165,  222 
Type,  Nephelite,  74,  76,  81,  103, 

104,  109,  121,  16o,  180,  181, 

222 
Type,    Sodium    Periodate,    103, 

104,  109,  165 
Type,  Tourmaline,  74,  76,  103, 

104,  109,  165,  178,  179,  230 

Unit  Prism,  191 
Unit  Pyramid,  194 
Unsymmetrical  Class,   167,   261 

Vegetable  Kingdom,  1 
Vertical  Axis,  Monoclinic,  41 
Vertical  Dome,  43,  44 


INDEX. 


299 


Vertical   Pinacoid,    11,    21,    42, 

44,  199 

Vertical  Prism,  189,  190 
Vertical     Quadrilateral     Prism, 

190 

Vertical  Ehombic  Prism,  190 
Vertical  Semi-Axis,  Orthorhom- 

bic,  50 

Vertical  Axis,  Tetragonal,  60 
Vertical  Axis,  Triclinie,  10 
Vesuvianite,  69,  74,  225 

Ward's  Natural  Science  Estab- 
lishment, viii 

Weiss,  C.  S.,  28,  29,  32,  33,  47, 
70,  84 


Weiss  Natation,  29-34,  47,  70, 
75,  84,  111,  132,  136 

Whewell-Grassmann-Miller  Sys- 
tem, 29 

Whitney,  J.  D.,  iii,  188 

Witherite,  149,  154,  258 

Wulfenite,  173 

Zigzag  Edges  of  the  Ehombo- 

hedron,  86,  90 
Zigzag  Edges  of  the  Scalenohe- 

dron,  89,  90 
Zircon,   18,  26,   61,   62,  70,   73. 

74,  206,  217,  219 
Zirconoid,  62,  195 
Zoology,  1 


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